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 2 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)\right)}{dx}\\=&cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)((\frac{(\frac{(\frac{3(\frac{(2 + 0)*\frac{1}{2}}{(2x + 6)^{\frac{1}{2}}} + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))}{(sqrt(2x + 6) + {2}^{x})})}{(3ln(sqrt(2x + 6) + {2}^{x}))} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}}{({x}^{x})})}{(ln({x}^{x}))}) + 1)\\=&\frac{cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(2x + 6)^{\frac{1}{2}}(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} + \frac{{2}^{x}ln(2)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} - \frac{log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}ln(x)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln({x}^{x})} - \frac{log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln({x}^{x})} + cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(2x + 6)^{\frac{1}{2}}(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} + \frac{{2}^{x}ln(2)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} - \frac{log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}ln(x)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln({x}^{x})} - \frac{log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln({x}^{x})} + cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)\right)}{dx}\\=&\frac{(\frac{\frac{-1}{2}(2 + 0)}{(2x + 6)^{\frac{3}{2}}})cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} + \frac{(\frac{-(\frac{(2 + 0)*\frac{1}{2}}{(2x + 6)^{\frac{1}{2}}} + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))}{(sqrt(2x + 6) + {2}^{x})^{2}})cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(2x + 6)^{\frac{1}{2}}ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} + \frac{-(\frac{(2 + 0)*\frac{1}{2}}{(2x + 6)^{\frac{1}{2}}} + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(2x + 6)^{\frac{1}{2}}(sqrt(2x + 6) + {2}^{x})ln^{2}(sqrt(2x + 6) + {2}^{x})(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} + \frac{-({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(2x + 6)^{\frac{1}{2}}(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})({x}^{x})} + \frac{-sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)((\frac{(\frac{(\frac{3(\frac{(2 + 0)*\frac{1}{2}}{(2x + 6)^{\frac{1}{2}}} + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))}{(sqrt(2x + 6) + {2}^{x})})}{(3ln(sqrt(2x + 6) + {2}^{x}))} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}}{({x}^{x})})}{(ln({x}^{x}))}) + 1)}{(2x + 6)^{\frac{1}{2}}(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} + \frac{(\frac{-(\frac{(2 + 0)*\frac{1}{2}}{(2x + 6)^{\frac{1}{2}}} + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))}{(sqrt(2x + 6) + {2}^{x})^{2}}){2}^{x}ln(2)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} + \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(2)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} + \frac{{2}^{x}*0cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})(2)ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} + \frac{{2}^{x}ln(2)*-(\frac{(2 + 0)*\frac{1}{2}}{(2x + 6)^{\frac{1}{2}}} + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln^{2}(sqrt(2x + 6) + {2}^{x})(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} + \frac{{2}^{x}ln(2)*-({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})({x}^{x})} + \frac{{2}^{x}ln(2)*-sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)((\frac{(\frac{(\frac{3(\frac{(2 + 0)*\frac{1}{2}}{(2x + 6)^{\frac{1}{2}}} + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))}{(sqrt(2x + 6) + {2}^{x})})}{(3ln(sqrt(2x + 6) + {2}^{x}))} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}}{({x}^{x})})}{(ln({x}^{x}))}) + 1)}{(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} - \frac{(\frac{(\frac{(\frac{3(\frac{(2 + 0)*\frac{1}{2}}{(2x + 6)^{\frac{1}{2}}} + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))}{(sqrt(2x + 6) + {2}^{x})})}{(3ln(sqrt(2x + 6) + {2}^{x}))} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}}{({x}^{x})})}{(ln({x}^{x}))})ln(x)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln({x}^{x})} - \frac{log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(x)ln({x}^{x})} - \frac{log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}ln(x)*-({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln^{2}({x}^{x})({x}^{x})} - \frac{log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}ln(x)*-sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)((\frac{(\frac{(\frac{3(\frac{(2 + 0)*\frac{1}{2}}{(2x + 6)^{\frac{1}{2}}} + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))}{(sqrt(2x + 6) + {2}^{x})})}{(3ln(sqrt(2x + 6) + {2}^{x}))} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}}{({x}^{x})})}{(ln({x}^{x}))}) + 1)}{ln({x}^{x})} - \frac{(\frac{(\frac{(\frac{3(\frac{(2 + 0)*\frac{1}{2}}{(2x + 6)^{\frac{1}{2}}} + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))}{(sqrt(2x + 6) + {2}^{x})})}{(3ln(sqrt(2x + 6) + {2}^{x}))} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}}{({x}^{x})})}{(ln({x}^{x}))})cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln({x}^{x})} - \frac{log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}*-({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln^{2}({x}^{x})({x}^{x})} - \frac{log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}*-sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)((\frac{(\frac{(\frac{3(\frac{(2 + 0)*\frac{1}{2}}{(2x + 6)^{\frac{1}{2}}} + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))}{(sqrt(2x + 6) + {2}^{x})})}{(3ln(sqrt(2x + 6) + {2}^{x}))} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}}{({x}^{x})})}{(ln({x}^{x}))}) + 1)}{ln({x}^{x})} + -sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)((\frac{(\frac{(\frac{3(\frac{(2 + 0)*\frac{1}{2}}{(2x + 6)^{\frac{1}{2}}} + ({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)})))}{(sqrt(2x + 6) + {2}^{x})})}{(3ln(sqrt(2x + 6) + {2}^{x}))} - \frac{(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}}{({x}^{x})})}{(ln({x}^{x}))}) + 1)\\=&\frac{-cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(2x + 6)^{\frac{3}{2}}(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} - \frac{cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})^{2}(2x + 6)ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} - \frac{2 * {2}^{x}ln(2)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})^{2}(2x + 6)^{\frac{1}{2}}ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} - \frac{cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})^{2}(2x + 6)ln^{2}(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} - \frac{{2}^{x}ln(2)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})^{2}(2x + 6)^{\frac{1}{2}}ln^{2}(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} - \frac{ln(x)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})(2x + 6)^{\frac{1}{2}}ln^{2}({x}^{x})ln(sqrt(2x + 6) + {2}^{x})} - \frac{cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})(2x + 6)^{\frac{1}{2}}ln^{2}({x}^{x})ln(sqrt(2x + 6) + {2}^{x})} - \frac{sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(2x + 6)(sqrt(2x + 6) + {2}^{x})^{2}ln^{2}(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})} - \frac{{2}^{x}ln(2)sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})^{2}(2x + 6)^{\frac{1}{2}}ln^{2}(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})} + \frac{log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}ln(x)sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})(2x + 6)^{\frac{1}{2}}ln^{2}({x}^{x})ln(sqrt(2x + 6) + {2}^{x})} + \frac{log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})(2x + 6)^{\frac{1}{2}}ln^{2}({x}^{x})ln(sqrt(2x + 6) + {2}^{x})} - \frac{2sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(2x + 6)^{\frac{1}{2}}(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} - \frac{{2}^{(2x)}ln^{2}(2)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})^{2}ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} + \frac{{2}^{x}ln^{2}(2)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} - \frac{{2}^{x}ln(2)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})^{2}(2x + 6)^{\frac{1}{2}}ln^{2}(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} - \frac{{2}^{(2x)}ln^{2}(2)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})^{2}ln^{2}(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} - \frac{{2}^{x}ln(x)ln(2)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})ln(sqrt(2x + 6) + {2}^{x})} - \frac{{2}^{x}ln(2)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})ln(sqrt(2x + 6) + {2}^{x})} - \frac{{2}^{x}ln(2)sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})^{2}(2x + 6)^{\frac{1}{2}}ln^{2}(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})} - \frac{{2}^{(2x)}ln^{2}(2)sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})^{2}ln^{2}(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})} + \frac{{2}^{x}log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}ln(x)ln(2)sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})} + \frac{{2}^{x}log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}ln(2)sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})} - \frac{{2}^{x}ln(2)sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln({x}^{x})ln(sqrt(2x + 6) + {2}^{x})} - \frac{ln(x)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(2x + 6)^{\frac{1}{2}}(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})} - \frac{{2}^{x}ln(2)ln(x)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}ln^{2}(x)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}ln(x)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln^{2}({x}^{x})} - \frac{log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{xln({x}^{x})} + \frac{log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}ln(x)sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(2x + 6)^{\frac{1}{2}}(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})} + \frac{{2}^{x}log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}ln(2)ln(x)sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})} - \frac{{\left(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}\right)}^{2}ln^{2}(x)sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln^{2}({x}^{x})} - \frac{{\left(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}\right)}^{2}ln(x)sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}ln(x)sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln({x}^{x})} - \frac{cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(2x + 6)^{\frac{1}{2}}(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})} - \frac{{2}^{x}ln(2)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}ln(x)cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}cos(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln^{2}({x}^{x})} + \frac{log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(2x + 6)^{\frac{1}{2}}(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})} + \frac{{2}^{x}log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}ln(2)sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln^{2}({x}^{x})} - \frac{{\left(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}\right)}^{2}ln(x)sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln^{2}({x}^{x})} - \frac{{\left(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}\right)}^{2}sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln^{2}({x}^{x})} + \frac{2log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})}sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{ln({x}^{x})} - \frac{{2}^{x}ln(2)sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)}{(sqrt(2x + 6) + {2}^{x})ln(sqrt(2x + 6) + {2}^{x})ln({x}^{x})} - sin(log_{{x}^{x}}^{3ln(sqrt(2x + 6) + {2}^{x})} + x)\\ \end{split}\end{equation} \]