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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ cos(x)sin(x)ln(x){\frac{1}{2}}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {\frac{1}{2}}^{x}ln(x)sin(x)cos(x)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {\frac{1}{2}}^{x}ln(x)sin(x)cos(x)\right)}{dx}\\=&({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(x)sin(x)cos(x) + \frac{{\frac{1}{2}}^{x}sin(x)cos(x)}{(x)} + {\frac{1}{2}}^{x}ln(x)cos(x)cos(x) + {\frac{1}{2}}^{x}ln(x)sin(x)*-sin(x)\\=&{\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)sin(x)cos(x) + \frac{{\frac{1}{2}}^{x}sin(x)cos(x)}{x} + {\frac{1}{2}}^{x}ln(x)cos^{2}(x) - {\frac{1}{2}}^{x}ln(x)sin^{2}(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)sin(x)cos(x) + \frac{{\frac{1}{2}}^{x}sin(x)cos(x)}{x} + {\frac{1}{2}}^{x}ln(x)cos^{2}(x) - {\frac{1}{2}}^{x}ln(x)sin^{2}(x)\right)}{dx}\\=&({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(\frac{1}{2})ln(x)sin(x)cos(x) + \frac{{\frac{1}{2}}^{x}*0ln(x)sin(x)cos(x)}{(\frac{1}{2})} + \frac{{\frac{1}{2}}^{x}ln(\frac{1}{2})sin(x)cos(x)}{(x)} + {\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)cos(x)cos(x) + {\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)sin(x)*-sin(x) + \frac{-{\frac{1}{2}}^{x}sin(x)cos(x)}{x^{2}} + \frac{({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))sin(x)cos(x)}{x} + \frac{{\frac{1}{2}}^{x}cos(x)cos(x)}{x} + \frac{{\frac{1}{2}}^{x}sin(x)*-sin(x)}{x} + ({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(x)cos^{2}(x) + \frac{{\frac{1}{2}}^{x}cos^{2}(x)}{(x)} + {\frac{1}{2}}^{x}ln(x)*-2cos(x)sin(x) - ({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(x)sin^{2}(x) - \frac{{\frac{1}{2}}^{x}sin^{2}(x)}{(x)} - {\frac{1}{2}}^{x}ln(x)*2sin(x)cos(x)\\=&{\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})ln(x)sin(x)cos(x) + \frac{2 * {\frac{1}{2}}^{x}ln(\frac{1}{2})sin(x)cos(x)}{x} + {\frac{1}{2}}^{x}ln(x)ln(\frac{1}{2})cos^{2}(x) - 2 * {\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)sin^{2}(x) - \frac{{\frac{1}{2}}^{x}sin(x)cos(x)}{x^{2}} + \frac{2 * {\frac{1}{2}}^{x}cos^{2}(x)}{x} - \frac{2 * {\frac{1}{2}}^{x}sin^{2}(x)}{x} + {\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)cos^{2}(x) - 4 * {\frac{1}{2}}^{x}ln(x)sin(x)cos(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})ln(x)sin(x)cos(x) + \frac{2 * {\frac{1}{2}}^{x}ln(\frac{1}{2})sin(x)cos(x)}{x} + {\frac{1}{2}}^{x}ln(x)ln(\frac{1}{2})cos^{2}(x) - 2 * {\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)sin^{2}(x) - \frac{{\frac{1}{2}}^{x}sin(x)cos(x)}{x^{2}} + \frac{2 * {\frac{1}{2}}^{x}cos^{2}(x)}{x} - \frac{2 * {\frac{1}{2}}^{x}sin^{2}(x)}{x} + {\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)cos^{2}(x) - 4 * {\frac{1}{2}}^{x}ln(x)sin(x)cos(x)\right)}{dx}\\=&({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln^{2}(\frac{1}{2})ln(x)sin(x)cos(x) + \frac{{\frac{1}{2}}^{x}*2ln(\frac{1}{2})*0ln(x)sin(x)cos(x)}{(\frac{1}{2})} + \frac{{\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})sin(x)cos(x)}{(x)} + {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})ln(x)cos(x)cos(x) + {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})ln(x)sin(x)*-sin(x) + \frac{2*-{\frac{1}{2}}^{x}ln(\frac{1}{2})sin(x)cos(x)}{x^{2}} + \frac{2({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(\frac{1}{2})sin(x)cos(x)}{x} + \frac{2 * {\frac{1}{2}}^{x}*0sin(x)cos(x)}{x(\frac{1}{2})} + \frac{2 * {\frac{1}{2}}^{x}ln(\frac{1}{2})cos(x)cos(x)}{x} + \frac{2 * {\frac{1}{2}}^{x}ln(\frac{1}{2})sin(x)*-sin(x)}{x} + ({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(x)ln(\frac{1}{2})cos^{2}(x) + \frac{{\frac{1}{2}}^{x}ln(\frac{1}{2})cos^{2}(x)}{(x)} + \frac{{\frac{1}{2}}^{x}ln(x)*0cos^{2}(x)}{(\frac{1}{2})} + {\frac{1}{2}}^{x}ln(x)ln(\frac{1}{2})*-2cos(x)sin(x) - 2({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(\frac{1}{2})ln(x)sin^{2}(x) - \frac{2 * {\frac{1}{2}}^{x}*0ln(x)sin^{2}(x)}{(\frac{1}{2})} - \frac{2 * {\frac{1}{2}}^{x}ln(\frac{1}{2})sin^{2}(x)}{(x)} - 2 * {\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)*2sin(x)cos(x) - \frac{-2 * {\frac{1}{2}}^{x}sin(x)cos(x)}{x^{3}} - \frac{({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))sin(x)cos(x)}{x^{2}} - \frac{{\frac{1}{2}}^{x}cos(x)cos(x)}{x^{2}} - \frac{{\frac{1}{2}}^{x}sin(x)*-sin(x)}{x^{2}} + \frac{2*-{\frac{1}{2}}^{x}cos^{2}(x)}{x^{2}} + \frac{2({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))cos^{2}(x)}{x} + \frac{2 * {\frac{1}{2}}^{x}*-2cos(x)sin(x)}{x} - \frac{2*-{\frac{1}{2}}^{x}sin^{2}(x)}{x^{2}} - \frac{2({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))sin^{2}(x)}{x} - \frac{2 * {\frac{1}{2}}^{x}*2sin(x)cos(x)}{x} + ({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(\frac{1}{2})ln(x)cos^{2}(x) + \frac{{\frac{1}{2}}^{x}*0ln(x)cos^{2}(x)}{(\frac{1}{2})} + \frac{{\frac{1}{2}}^{x}ln(\frac{1}{2})cos^{2}(x)}{(x)} + {\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)*-2cos(x)sin(x) - 4({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(x)sin(x)cos(x) - \frac{4 * {\frac{1}{2}}^{x}sin(x)cos(x)}{(x)} - 4 * {\frac{1}{2}}^{x}ln(x)cos(x)cos(x) - 4 * {\frac{1}{2}}^{x}ln(x)sin(x)*-sin(x)\\=&{\frac{1}{2}}^{x}ln^{3}(\frac{1}{2})ln(x)sin(x)cos(x) + \frac{3 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})sin(x)cos(x)}{x} + {\frac{1}{2}}^{x}ln(x)ln^{2}(\frac{1}{2})cos^{2}(x) - 2 * {\frac{1}{2}}^{x}ln(x)ln(\frac{1}{2})sin(x)cos(x) - \frac{3 * {\frac{1}{2}}^{x}ln(\frac{1}{2})sin(x)cos(x)}{x^{2}} - \frac{12 * {\frac{1}{2}}^{x}sin(x)cos(x)}{x} + \frac{6 * {\frac{1}{2}}^{x}ln(\frac{1}{2})cos^{2}(x)}{x} - \frac{6 * {\frac{1}{2}}^{x}ln(\frac{1}{2})sin^{2}(x)}{x} + 2 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})ln(x)cos^{2}(x) - 4 * {\frac{1}{2}}^{x}ln(x)cos^{2}(x) - 10 * {\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)sin(x)cos(x) - 3 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})ln(x)sin^{2}(x) + 4 * {\frac{1}{2}}^{x}ln(x)sin^{2}(x) + \frac{2 * {\frac{1}{2}}^{x}sin(x)cos(x)}{x^{3}} - \frac{3 * {\frac{1}{2}}^{x}cos^{2}(x)}{x^{2}} + \frac{3 * {\frac{1}{2}}^{x}sin^{2}(x)}{x^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( {\frac{1}{2}}^{x}ln^{3}(\frac{1}{2})ln(x)sin(x)cos(x) + \frac{3 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})sin(x)cos(x)}{x} + {\frac{1}{2}}^{x}ln(x)ln^{2}(\frac{1}{2})cos^{2}(x) - 2 * {\frac{1}{2}}^{x}ln(x)ln(\frac{1}{2})sin(x)cos(x) - \frac{3 * {\frac{1}{2}}^{x}ln(\frac{1}{2})sin(x)cos(x)}{x^{2}} - \frac{12 * {\frac{1}{2}}^{x}sin(x)cos(x)}{x} + \frac{6 * {\frac{1}{2}}^{x}ln(\frac{1}{2})cos^{2}(x)}{x} - \frac{6 * {\frac{1}{2}}^{x}ln(\frac{1}{2})sin^{2}(x)}{x} + 2 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})ln(x)cos^{2}(x) - 4 * {\frac{1}{2}}^{x}ln(x)cos^{2}(x) - 10 * {\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)sin(x)cos(x) - 3 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})ln(x)sin^{2}(x) + 4 * {\frac{1}{2}}^{x}ln(x)sin^{2}(x) + \frac{2 * {\frac{1}{2}}^{x}sin(x)cos(x)}{x^{3}} - \frac{3 * {\frac{1}{2}}^{x}cos^{2}(x)}{x^{2}} + \frac{3 * {\frac{1}{2}}^{x}sin^{2}(x)}{x^{2}}\right)}{dx}\\=&({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln^{3}(\frac{1}{2})ln(x)sin(x)cos(x) + \frac{{\frac{1}{2}}^{x}*3ln^{2}(\frac{1}{2})*0ln(x)sin(x)cos(x)}{(\frac{1}{2})} + \frac{{\frac{1}{2}}^{x}ln^{3}(\frac{1}{2})sin(x)cos(x)}{(x)} + {\frac{1}{2}}^{x}ln^{3}(\frac{1}{2})ln(x)cos(x)cos(x) + {\frac{1}{2}}^{x}ln^{3}(\frac{1}{2})ln(x)sin(x)*-sin(x) + \frac{3*-{\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})sin(x)cos(x)}{x^{2}} + \frac{3({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln^{2}(\frac{1}{2})sin(x)cos(x)}{x} + \frac{3 * {\frac{1}{2}}^{x}*2ln(\frac{1}{2})*0sin(x)cos(x)}{x(\frac{1}{2})} + \frac{3 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})cos(x)cos(x)}{x} + \frac{3 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})sin(x)*-sin(x)}{x} + ({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(x)ln^{2}(\frac{1}{2})cos^{2}(x) + \frac{{\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})cos^{2}(x)}{(x)} + \frac{{\frac{1}{2}}^{x}ln(x)*2ln(\frac{1}{2})*0cos^{2}(x)}{(\frac{1}{2})} + {\frac{1}{2}}^{x}ln(x)ln^{2}(\frac{1}{2})*-2cos(x)sin(x) - 2({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(x)ln(\frac{1}{2})sin(x)cos(x) - \frac{2 * {\frac{1}{2}}^{x}ln(\frac{1}{2})sin(x)cos(x)}{(x)} - \frac{2 * {\frac{1}{2}}^{x}ln(x)*0sin(x)cos(x)}{(\frac{1}{2})} - 2 * {\frac{1}{2}}^{x}ln(x)ln(\frac{1}{2})cos(x)cos(x) - 2 * {\frac{1}{2}}^{x}ln(x)ln(\frac{1}{2})sin(x)*-sin(x) - \frac{3*-2 * {\frac{1}{2}}^{x}ln(\frac{1}{2})sin(x)cos(x)}{x^{3}} - \frac{3({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(\frac{1}{2})sin(x)cos(x)}{x^{2}} - \frac{3 * {\frac{1}{2}}^{x}*0sin(x)cos(x)}{x^{2}(\frac{1}{2})} - \frac{3 * {\frac{1}{2}}^{x}ln(\frac{1}{2})cos(x)cos(x)}{x^{2}} - \frac{3 * {\frac{1}{2}}^{x}ln(\frac{1}{2})sin(x)*-sin(x)}{x^{2}} - \frac{12*-{\frac{1}{2}}^{x}sin(x)cos(x)}{x^{2}} - \frac{12({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))sin(x)cos(x)}{x} - \frac{12 * {\frac{1}{2}}^{x}cos(x)cos(x)}{x} - \frac{12 * {\frac{1}{2}}^{x}sin(x)*-sin(x)}{x} + \frac{6*-{\frac{1}{2}}^{x}ln(\frac{1}{2})cos^{2}(x)}{x^{2}} + \frac{6({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(\frac{1}{2})cos^{2}(x)}{x} + \frac{6 * {\frac{1}{2}}^{x}*0cos^{2}(x)}{x(\frac{1}{2})} + \frac{6 * {\frac{1}{2}}^{x}ln(\frac{1}{2})*-2cos(x)sin(x)}{x} - \frac{6*-{\frac{1}{2}}^{x}ln(\frac{1}{2})sin^{2}(x)}{x^{2}} - \frac{6({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(\frac{1}{2})sin^{2}(x)}{x} - \frac{6 * {\frac{1}{2}}^{x}*0sin^{2}(x)}{x(\frac{1}{2})} - \frac{6 * {\frac{1}{2}}^{x}ln(\frac{1}{2})*2sin(x)cos(x)}{x} + 2({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln^{2}(\frac{1}{2})ln(x)cos^{2}(x) + \frac{2 * {\frac{1}{2}}^{x}*2ln(\frac{1}{2})*0ln(x)cos^{2}(x)}{(\frac{1}{2})} + \frac{2 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})cos^{2}(x)}{(x)} + 2 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})ln(x)*-2cos(x)sin(x) - 4({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(x)cos^{2}(x) - \frac{4 * {\frac{1}{2}}^{x}cos^{2}(x)}{(x)} - 4 * {\frac{1}{2}}^{x}ln(x)*-2cos(x)sin(x) - 10({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(\frac{1}{2})ln(x)sin(x)cos(x) - \frac{10 * {\frac{1}{2}}^{x}*0ln(x)sin(x)cos(x)}{(\frac{1}{2})} - \frac{10 * {\frac{1}{2}}^{x}ln(\frac{1}{2})sin(x)cos(x)}{(x)} - 10 * {\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)cos(x)cos(x) - 10 * {\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)sin(x)*-sin(x) - 3({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln^{2}(\frac{1}{2})ln(x)sin^{2}(x) - \frac{3 * {\frac{1}{2}}^{x}*2ln(\frac{1}{2})*0ln(x)sin^{2}(x)}{(\frac{1}{2})} - \frac{3 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})sin^{2}(x)}{(x)} - 3 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})ln(x)*2sin(x)cos(x) + 4({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))ln(x)sin^{2}(x) + \frac{4 * {\frac{1}{2}}^{x}sin^{2}(x)}{(x)} + 4 * {\frac{1}{2}}^{x}ln(x)*2sin(x)cos(x) + \frac{2*-3 * {\frac{1}{2}}^{x}sin(x)cos(x)}{x^{4}} + \frac{2({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))sin(x)cos(x)}{x^{3}} + \frac{2 * {\frac{1}{2}}^{x}cos(x)cos(x)}{x^{3}} + \frac{2 * {\frac{1}{2}}^{x}sin(x)*-sin(x)}{x^{3}} - \frac{3*-2 * {\frac{1}{2}}^{x}cos^{2}(x)}{x^{3}} - \frac{3({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))cos^{2}(x)}{x^{2}} - \frac{3 * {\frac{1}{2}}^{x}*-2cos(x)sin(x)}{x^{2}} + \frac{3*-2 * {\frac{1}{2}}^{x}sin^{2}(x)}{x^{3}} + \frac{3({\frac{1}{2}}^{x}((1)ln(\frac{1}{2}) + \frac{(x)(0)}{(\frac{1}{2})}))sin^{2}(x)}{x^{2}} + \frac{3 * {\frac{1}{2}}^{x}*2sin(x)cos(x)}{x^{2}}\\=&{\frac{1}{2}}^{x}ln^{4}(\frac{1}{2})ln(x)sin(x)cos(x) + \frac{4 * {\frac{1}{2}}^{x}ln^{3}(\frac{1}{2})sin(x)cos(x)}{x} + {\frac{1}{2}}^{x}ln(x)ln^{3}(\frac{1}{2})cos^{2}(x) - 2 * {\frac{1}{2}}^{x}ln(x)ln^{2}(\frac{1}{2})sin(x)cos(x) - \frac{6 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})sin(x)cos(x)}{x^{2}} - \frac{48 * {\frac{1}{2}}^{x}ln(\frac{1}{2})sin(x)cos(x)}{x} + \frac{12 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})cos^{2}(x)}{x} + \frac{8 * {\frac{1}{2}}^{x}ln(\frac{1}{2})sin(x)cos(x)}{x^{3}} + 3 * {\frac{1}{2}}^{x}ln^{3}(\frac{1}{2})ln(x)cos^{2}(x) - 10 * {\frac{1}{2}}^{x}ln(x)ln(\frac{1}{2})cos^{2}(x) - 22 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})ln(x)sin(x)cos(x) + 16 * {\frac{1}{2}}^{x}ln(x)sin(x)cos(x) - 6 * {\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)cos^{2}(x) + 2 * {\frac{1}{2}}^{x}ln(x)ln(\frac{1}{2})sin^{2}(x) - \frac{12 * {\frac{1}{2}}^{x}ln^{2}(\frac{1}{2})sin^{2}(x)}{x} + \frac{24 * {\frac{1}{2}}^{x}sin(x)cos(x)}{x^{2}} - \frac{12 * {\frac{1}{2}}^{x}ln(\frac{1}{2})cos^{2}(x)}{x^{2}} + \frac{12 * {\frac{1}{2}}^{x}ln(\frac{1}{2})sin^{2}(x)}{x^{2}} - \frac{16 * {\frac{1}{2}}^{x}cos^{2}(x)}{x} - \frac{6 * {\frac{1}{2}}^{x}sin(x)cos(x)}{x^{4}} - \frac{8 * {\frac{1}{2}}^{x}sin^{2}(x)}{x^{3}} - 4 * {\frac{1}{2}}^{x}ln^{3}(\frac{1}{2})ln(x)sin^{2}(x) + 14 * {\frac{1}{2}}^{x}ln(\frac{1}{2})ln(x)sin^{2}(x) + \frac{16 * {\frac{1}{2}}^{x}sin^{2}(x)}{x} + \frac{8 * {\frac{1}{2}}^{x}cos^{2}(x)}{x^{3}}\\ \end{split}\end{equation} \]