Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {a}^{(xe^{x} + {2}^{(ae^{x})})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {a}^{(xe^{x} + {2}^{(ae^{x})})}\right)}{dx}\\=&({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))\\=&{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a)ln(2)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a)ln(2)\right)}{dx}\\=&({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{x}ln(a) + {a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + \frac{{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}*0}{(a)} + {a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + x({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{x}ln(a) + x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + \frac{x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}*0}{(a)} + a({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a)ln(2) + a{2}^{(ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{x}ln(a)ln(2) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a)ln(2) + \frac{a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}*0ln(2)}{(a)} + \frac{a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a)*0}{(2)}\\=&{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + 2x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln(2)ln^{2}(a) + 2{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)ln(2) + x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln(a) + a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln^{2}(a) + a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{x}ln(a)ln(2)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( {a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + 2x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln(2)ln^{2}(a) + 2{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)ln(2) + x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln(a) + a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln^{2}(a) + a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{x}ln(a)ln(2)\right)}{dx}\\=&({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln^{2}(a) + {a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln^{2}(a) + \frac{{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*2ln(a)*0}{(a)} + 2{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + 2x({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln^{2}(a) + 2x{a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln^{2}(a) + \frac{2x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*2ln(a)*0}{(a)} + a({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln(2)ln^{2}(a) + a{2}^{(ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln(2)ln^{2}(a) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln(2)ln^{2}(a) + \frac{a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*0ln^{2}(a)}{(2)} + \frac{a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln(2)*2ln(a)*0}{(a)} + 2({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{x}ln(a) + 2{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + \frac{2{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}*0}{(a)} + 2x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + x^{2}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln^{2}(a) + x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln^{2}(a) + \frac{x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*2ln(a)*0}{(a)} + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)ln(2) + ax({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)ln(2) + ax{2}^{(ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln^{2}(a)ln(2) + ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln^{2}(a)ln(2) + \frac{ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*2ln(a)*0ln(2)}{(a)} + \frac{ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)*0}{(2)} + {a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + x({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{x}ln(a) + x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + \frac{x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}*0}{(a)} + a^{2}({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln(a) + a^{2}{2}^{(ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln^{2}(2)ln(a) + a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln^{2}(2)ln(a) + \frac{a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*2ln(2)*0ln(a)}{(2)} + \frac{a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)*0}{(a)} + a({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)})){2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + a{a}^{(xe^{x} + {2}^{(ae^{x})})}({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)}))e^{{x}*{2}}ln^{2}(a)ln(2) + a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}*2e^{x}e^{x}ln^{2}(a)ln(2) + \frac{a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}*2ln(a)*0ln(2)}{(a)} + \frac{a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)*0}{(2)} + a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + ax({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)})){2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + ax{a}^{(xe^{x} + {2}^{(ae^{x})})}({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)}))e^{{x}*{2}}ln^{2}(a)ln(2) + ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}*2e^{x}e^{x}ln^{2}(a)ln(2) + \frac{ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}*2ln(a)*0ln(2)}{(a)} + \frac{ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)*0}{(2)} + a^{2}({2}^{(2(ae^{x}))}((2(ae^{x}))ln(2) + \frac{(2(ae^{x}))(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln^{2}(a) + a^{2}{2}^{(2(ae^{x}))}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln^{2}(2)ln^{2}(a) + a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln^{2}(2)ln^{2}(a) + \frac{a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*2ln(2)*0ln^{2}(a)}{(2)} + \frac{a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)*2ln(a)*0}{(a)} + a({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)})){2}^{(ae^{x})}e^{x}ln(a)ln(2) + a{a}^{(xe^{x} + {2}^{(ae^{x})})}({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)}))e^{x}ln(a)ln(2) + a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{x}ln(a)ln(2) + \frac{a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{x}*0ln(2)}{(a)} + \frac{a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{x}ln(a)*0}{(2)}\\=&{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a) + 3x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln(2)ln^{3}(a) + 6{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + 3x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a) + 2ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln(2) + 9x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + 2a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)ln^{2}(a) + 2a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)ln(2) + 4ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)ln(2) + 2a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)ln^{3}(a) + 4a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln(2)ln^{2}(a) + 3{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + x^{3}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a) + ax^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln(2) + 3x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)ln(2) + 2a^{2}x{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)ln^{2}(a) + 2ax^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)ln(2) + 2a^{2}x{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + 3ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)ln(2) + x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + a^{3}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln(a) + a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{2}(a)ln^{2}(2) + a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{2}(a)ln^{2}(2) + a^{3}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln^{2}(a) + 3a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln(a) + 4a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + 3ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + 2a^{3}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln^{2}(a) + a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + a^{3}{2}^{(3ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln^{3}(a) + 2a^{2}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln^{2}(a) + a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln^{2}(a) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a)ln(2)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( {a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a) + 3x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln(2)ln^{3}(a) + 6{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + 3x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a) + 2ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln(2) + 9x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + 2a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)ln^{2}(a) + 2a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)ln(2) + 4ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)ln(2) + 2a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)ln^{3}(a) + 4a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln(2)ln^{2}(a) + 3{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + x^{3}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a) + ax^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln(2) + 3x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)ln(2) + 2a^{2}x{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)ln^{2}(a) + 2ax^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)ln(2) + 2a^{2}x{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + 3ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)ln(2) + x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + a^{3}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln(a) + a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{2}(a)ln^{2}(2) + a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{2}(a)ln^{2}(2) + a^{3}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln^{2}(a) + 3a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln(a) + 4a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + 3ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + 2a^{3}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln^{2}(a) + a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + a^{3}{2}^{(3ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln^{3}(a) + 2a^{2}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln^{2}(a) + a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln^{2}(a) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a)ln(2)\right)}{dx}\\=&({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{3}}ln^{3}(a) + {a}^{(xe^{x} + {2}^{(ae^{x})})}*3e^{{x}*{2}}e^{x}ln^{3}(a) + \frac{{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}*3ln^{2}(a)*0}{(a)} + 3{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a) + 3x({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{3}}ln^{3}(a) + 3x{a}^{(xe^{x} + {2}^{(ae^{x})})}*3e^{{x}*{2}}e^{x}ln^{3}(a) + \frac{3x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}*3ln^{2}(a)*0}{(a)} + a({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln(2)ln^{3}(a) + a{2}^{(ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{3}}ln(2)ln^{3}(a) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*3e^{{x}*{2}}e^{x}ln(2)ln^{3}(a) + \frac{a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}*0ln^{3}(a)}{(2)} + \frac{a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln(2)*3ln^{2}(a)*0}{(a)} + 6({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln^{2}(a) + 6{a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln^{2}(a) + \frac{6{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*2ln(a)*0}{(a)} + 3*2x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a) + 3x^{2}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{3}}ln^{3}(a) + 3x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}*3e^{{x}*{2}}e^{x}ln^{3}(a) + \frac{3x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}*3ln^{2}(a)*0}{(a)} + 2a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln(2) + 2ax({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln(2) + 2ax{2}^{(ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{3}}ln^{3}(a)ln(2) + 2ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*3e^{{x}*{2}}e^{x}ln^{3}(a)ln(2) + \frac{2ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}*3ln^{2}(a)*0ln(2)}{(a)} + \frac{2ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)*0}{(2)} + 9{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + 9x({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln^{2}(a) + 9x{a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln^{2}(a) + \frac{9x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*2ln(a)*0}{(a)} + 2a^{2}({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)ln^{2}(a) + 2a^{2}{2}^{(ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{3}}ln^{2}(2)ln^{2}(a) + 2a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*3e^{{x}*{2}}e^{x}ln^{2}(2)ln^{2}(a) + \frac{2a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}*2ln(2)*0ln^{2}(a)}{(2)} + \frac{2a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)*2ln(a)*0}{(a)} + 2a({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)})){2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)ln(2) + 2a{a}^{(xe^{x} + {2}^{(ae^{x})})}({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)}))e^{{x}*{3}}ln^{3}(a)ln(2) + 2a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}*3e^{{x}*{2}}e^{x}ln^{3}(a)ln(2) + \frac{2a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}*3ln^{2}(a)*0ln(2)}{(a)} + \frac{2a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)*0}{(2)} + 4a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)ln(2) + 4ax({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)})){2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)ln(2) + 4ax{a}^{(xe^{x} + {2}^{(ae^{x})})}({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)}))e^{{x}*{3}}ln^{3}(a)ln(2) + 4ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}*3e^{{x}*{2}}e^{x}ln^{3}(a)ln(2) + \frac{4ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}*3ln^{2}(a)*0ln(2)}{(a)} + \frac{4ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)*0}{(2)} + 2a^{2}({2}^{(2(ae^{x}))}((2(ae^{x}))ln(2) + \frac{(2(ae^{x}))(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)ln^{3}(a) + 2a^{2}{2}^{(2(ae^{x}))}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{3}}ln^{2}(2)ln^{3}(a) + 2a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}*3e^{{x}*{2}}e^{x}ln^{2}(2)ln^{3}(a) + \frac{2a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}*2ln(2)*0ln^{3}(a)}{(2)} + \frac{2a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)*3ln^{2}(a)*0}{(a)} + 4a({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln(2)ln^{2}(a) + 4a{2}^{(ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln(2)ln^{2}(a) + 4a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln(2)ln^{2}(a) + \frac{4a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*0ln^{2}(a)}{(2)} + \frac{4a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln(2)*2ln(a)*0}{(a)} + 3({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{x}ln(a) + 3{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + \frac{3{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}*0}{(a)} + 3x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a) + x^{3}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{3}}ln^{3}(a) + x^{3}{a}^{(xe^{x} + {2}^{(ae^{x})})}*3e^{{x}*{2}}e^{x}ln^{3}(a) + \frac{x^{3}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}*3ln^{2}(a)*0}{(a)} + a*2x{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln(2) + ax^{2}({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln(2) + ax^{2}{2}^{(ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{3}}ln^{3}(a)ln(2) + ax^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*3e^{{x}*{2}}e^{x}ln^{3}(a)ln(2) + \frac{ax^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}*3ln^{2}(a)*0ln(2)}{(a)} + \frac{ax^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)*0}{(2)} + 3*2x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + 3x^{2}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln^{2}(a) + 3x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln^{2}(a) + \frac{3x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*2ln(a)*0}{(a)} + a({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)ln(2) + a{2}^{(ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln^{2}(a)ln(2) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln^{2}(a)ln(2) + \frac{a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*2ln(a)*0ln(2)}{(a)} + \frac{a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)*0}{(2)} + 2a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)ln^{2}(a) + 2a^{2}x({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)ln^{2}(a) + 2a^{2}x{2}^{(ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{3}}ln^{2}(2)ln^{2}(a) + 2a^{2}x{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*3e^{{x}*{2}}e^{x}ln^{2}(2)ln^{2}(a) + \frac{2a^{2}x{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}*2ln(2)*0ln^{2}(a)}{(2)} + \frac{2a^{2}x{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)*2ln(a)*0}{(a)} + 2a*2x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)ln(2) + 2ax^{2}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)})){2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)ln(2) + 2ax^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)}))e^{{x}*{3}}ln^{3}(a)ln(2) + 2ax^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}*3e^{{x}*{2}}e^{x}ln^{3}(a)ln(2) + \frac{2ax^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}*3ln^{2}(a)*0ln(2)}{(a)} + \frac{2ax^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)*0}{(2)} + 2a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + 2a^{2}x({2}^{(2(ae^{x}))}((2(ae^{x}))ln(2) + \frac{(2(ae^{x}))(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + 2a^{2}x{2}^{(2(ae^{x}))}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + 2a^{2}x{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}*3e^{{x}*{2}}e^{x}ln^{3}(a)ln^{2}(2) + \frac{2a^{2}x{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}*3ln^{2}(a)*0ln^{2}(2)}{(a)} + \frac{2a^{2}x{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)*2ln(2)*0}{(2)} + 3a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)ln(2) + 3ax({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)ln(2) + 3ax{2}^{(ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln^{2}(a)ln(2) + 3ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln^{2}(a)ln(2) + \frac{3ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*2ln(a)*0ln(2)}{(a)} + \frac{3ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)*0}{(2)} + {a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + x({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{x}ln(a) + x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + \frac{x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}*0}{(a)} + a^{3}({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln(a) + a^{3}{2}^{(ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{3}}ln^{3}(2)ln(a) + a^{3}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*3e^{{x}*{2}}e^{x}ln^{3}(2)ln(a) + \frac{a^{3}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}*3ln^{2}(2)*0ln(a)}{(2)} + \frac{a^{3}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)*0}{(a)} + a^{2}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)})){2}^{(ae^{x})}e^{{x}*{3}}ln^{2}(a)ln^{2}(2) + a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)}))e^{{x}*{3}}ln^{2}(a)ln^{2}(2) + a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}*3e^{{x}*{2}}e^{x}ln^{2}(a)ln^{2}(2) + \frac{a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}*2ln(a)*0ln^{2}(2)}{(a)} + \frac{a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{2}(a)*2ln(2)*0}{(2)} + a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{2}(a)ln^{2}(2) + a^{2}x({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)})){2}^{(ae^{x})}e^{{x}*{3}}ln^{2}(a)ln^{2}(2) + a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)}))e^{{x}*{3}}ln^{2}(a)ln^{2}(2) + a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}*3e^{{x}*{2}}e^{x}ln^{2}(a)ln^{2}(2) + \frac{a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}*2ln(a)*0ln^{2}(2)}{(a)} + \frac{a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{2}(a)*2ln(2)*0}{(2)} + a^{3}({2}^{(2(ae^{x}))}((2(ae^{x}))ln(2) + \frac{(2(ae^{x}))(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln^{2}(a) + a^{3}{2}^{(2(ae^{x}))}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{3}}ln^{3}(2)ln^{2}(a) + a^{3}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}*3e^{{x}*{2}}e^{x}ln^{3}(2)ln^{2}(a) + \frac{a^{3}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}*3ln^{2}(2)*0ln^{2}(a)}{(2)} + \frac{a^{3}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)*2ln(a)*0}{(a)} + 3a^{2}({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln(a) + 3a^{2}{2}^{(ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln^{2}(2)ln(a) + 3a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln^{2}(2)ln(a) + \frac{3a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*2ln(2)*0ln(a)}{(2)} + \frac{3a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)*0}{(a)} + 4a({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)})){2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + 4a{a}^{(xe^{x} + {2}^{(ae^{x})})}({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)}))e^{{x}*{2}}ln^{2}(a)ln(2) + 4a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}*2e^{x}e^{x}ln^{2}(a)ln(2) + \frac{4a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}*2ln(a)*0ln(2)}{(a)} + \frac{4a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)*0}{(2)} + 3a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + 3ax({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)})){2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + 3ax{a}^{(xe^{x} + {2}^{(ae^{x})})}({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)}))e^{{x}*{2}}ln^{2}(a)ln(2) + 3ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}*2e^{x}e^{x}ln^{2}(a)ln(2) + \frac{3ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}*2ln(a)*0ln(2)}{(a)} + \frac{3ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)*0}{(2)} + 2a^{3}({2}^{(2ae^{x})}((2ae^{x})ln(2) + \frac{(2ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln^{2}(a) + 2a^{3}{2}^{(2ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{3}}ln^{3}(2)ln^{2}(a) + 2a^{3}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*3e^{{x}*{2}}e^{x}ln^{3}(2)ln^{2}(a) + \frac{2a^{3}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}*3ln^{2}(2)*0ln^{2}(a)}{(2)} + \frac{2a^{3}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)*2ln(a)*0}{(a)} + a^{2}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)})){2}^{(2ae^{x})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}({2}^{(2ae^{x})}((2ae^{x})ln(2) + \frac{(2ae^{x})(0)}{(2)}))e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}*3e^{{x}*{2}}e^{x}ln^{3}(a)ln^{2}(2) + \frac{a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{3}}*3ln^{2}(a)*0ln^{2}(2)}{(a)} + \frac{a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{3}}ln^{3}(a)*2ln(2)*0}{(2)} + a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + a^{2}x({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)})){2}^{(2ae^{x})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}({2}^{(2ae^{x})}((2ae^{x})ln(2) + \frac{(2ae^{x})(0)}{(2)}))e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}*3e^{{x}*{2}}e^{x}ln^{3}(a)ln^{2}(2) + \frac{a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{3}}*3ln^{2}(a)*0ln^{2}(2)}{(a)} + \frac{a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{3}}ln^{3}(a)*2ln(2)*0}{(2)} + a^{3}({2}^{(3ae^{x})}((3ae^{x})ln(2) + \frac{(3ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln^{3}(a) + a^{3}{2}^{(3ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{3}}ln^{3}(2)ln^{3}(a) + a^{3}{2}^{(3ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*3e^{{x}*{2}}e^{x}ln^{3}(2)ln^{3}(a) + \frac{a^{3}{2}^{(3ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}*3ln^{2}(2)*0ln^{3}(a)}{(2)} + \frac{a^{3}{2}^{(3ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)*3ln^{2}(a)*0}{(a)} + 2a^{2}({2}^{(2ae^{x})}((2ae^{x})ln(2) + \frac{(2ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln^{2}(a) + 2a^{2}{2}^{(2ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln^{2}(2)ln^{2}(a) + 2a^{2}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln^{2}(2)ln^{2}(a) + \frac{2a^{2}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*2ln(2)*0ln^{2}(a)}{(2)} + \frac{2a^{2}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)*2ln(a)*0}{(a)} + a^{2}({2}^{(2(ae^{x}))}((2(ae^{x}))ln(2) + \frac{(2(ae^{x}))(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln^{2}(a) + a^{2}{2}^{(2(ae^{x}))}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{{x}*{2}}ln^{2}(2)ln^{2}(a) + a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}*2e^{x}e^{x}ln^{2}(2)ln^{2}(a) + \frac{a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}*2ln(2)*0ln^{2}(a)}{(2)} + \frac{a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)*2ln(a)*0}{(a)} + a({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})){a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a)ln(2) + a{2}^{(ae^{x})}({a}^{(xe^{x} + {2}^{(ae^{x})})}((e^{x} + xe^{x} + ({2}^{(ae^{x})}((ae^{x})ln(2) + \frac{(ae^{x})(0)}{(2)})))ln(a) + \frac{(xe^{x} + {2}^{(ae^{x})})(0)}{(a)}))e^{x}ln(a)ln(2) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a)ln(2) + \frac{a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}*0ln(2)}{(a)} + \frac{a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a)*0}{(2)}\\=&{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(a) + 4x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(a) + a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln(2)ln^{4}(a) + 12{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a) + 6x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(a) + 3ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(a)ln(2) + 30x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a) + 3a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{2}(2)ln^{3}(a) + 3a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{4}}ln^{4}(a)ln(2) + 9ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{4}}ln^{4}(a)ln(2) + 3a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{2}(2)ln^{4}(a) + 9a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln(2)ln^{3}(a) + 24{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + 4x^{3}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(a) + 3ax^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(a)ln(2) + 24x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a) + 2a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln(2) + 6a^{2}x{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{2}(2)ln^{3}(a) + 9ax^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{4}}ln^{4}(a)ln(2) + 6a^{2}x{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(a)ln^{2}(2) + 17ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln(2) + 28x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + 3a^{3}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{3}(2)ln^{2}(a) + 3a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{4}}ln^{3}(a)ln^{2}(2) + 6a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{4}}ln^{3}(a)ln^{2}(2) + 3a^{3}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{3}(2)ln^{3}(a) + 17a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)ln^{2}(a) + 19a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)ln(2) + 31ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)ln(2) + 6a^{3}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{3}(2)ln^{3}(a) + 3a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{4}}ln^{4}(a)ln^{2}(2) + 6a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{4}}ln^{4}(a)ln^{2}(2) + 3a^{3}{2}^{(3ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{3}(2)ln^{4}(a) + 6a^{2}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)ln^{3}(a) + 9a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)ln^{3}(a) + 11a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln(2)ln^{2}(a) + 4{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + x^{4}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(a) + ax^{3}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(a)ln(2) + 6x^{3}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a) + 3a^{2}x^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{2}(2)ln^{3}(a) + 3ax^{3}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{4}}ln^{4}(a)ln(2) + 3a^{2}x^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(a)ln^{2}(2) + 6ax^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln(2) + 7x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a) + 5a{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)ln(2) + 3a^{3}x{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{3}(2)ln^{2}(a) + 3a^{2}x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{4}}ln^{3}(a)ln^{2}(2) + 3a^{3}x{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{3}(a)ln^{3}(2) + 12a^{2}x{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{2}(2)ln^{2}(a) + 12ax^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{3}(a)ln(2) + 2a^{2}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + 6a^{3}x{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{3}(2)ln^{3}(a) + 3a^{2}x^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{4}}ln^{4}(a)ln^{2}(2) + 3a^{3}x{2}^{(3ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(a)ln^{3}(2) + 6a^{2}x{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + 6a^{2}x{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + 7ax{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(a)ln(2) + x{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{x}ln(a) + a^{4}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(2)ln(a) + a^{3}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{4}}ln^{2}(a)ln^{3}(2) + a^{3}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{4}}ln^{2}(a)ln^{3}(2) + a^{4}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(2)ln^{2}(a) + 6a^{3}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln(a) + 7a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{2}(a)ln^{2}(2) + 6a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{3}}ln^{2}(a)ln^{2}(2) + 6a^{4}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(2)ln^{2}(a) + 3a^{3}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{4}}ln^{3}(a)ln^{3}(2) + 3a^{3}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{4}}ln^{3}(a)ln^{3}(2) + 6a^{4}{2}^{(3ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(2)ln^{3}(a) + 15a^{3}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln^{2}(a) + 3a^{3}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln^{2}(a) + 7a^{2}{2}^{(ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln(a) + 12a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + 7ax{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{{x}*{2}}ln^{2}(a)ln(2) + 7a^{2}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + 6a^{2}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(2ae^{x})}e^{{x}*{3}}ln^{3}(a)ln^{2}(2) + a^{3}{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(3ae^{x})}e^{{x}*{4}}ln^{4}(a)ln^{3}(2) + a^{3}x{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(3ae^{x})}e^{{x}*{4}}ln^{4}(a)ln^{3}(2) + a^{4}{2}^{(4ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{4}}ln^{4}(2)ln^{4}(a) + 6a^{3}{2}^{(3ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{3}}ln^{3}(2)ln^{3}(a) + 6a^{2}{2}^{(2ae^{x})}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln^{2}(a) + a^{2}{2}^{(2(ae^{x}))}{a}^{(xe^{x} + {2}^{(ae^{x})})}e^{{x}*{2}}ln^{2}(2)ln^{2}(a) + a{a}^{(xe^{x} + {2}^{(ae^{x})})}{2}^{(ae^{x})}e^{x}ln(a)ln(2)\\ \end{split}\end{equation} \]