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) + log_{7}^{x}{\frac{1}{x}}^{sqrt(x)} - Igx\ with\ respect\ to\ x：\\\end{split}\end{equation}
\begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = cos(x) + {\frac{1}{x}}^{sqrt(x)}log_{7}^{x} - Igx\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( cos(x) + {\frac{1}{x}}^{sqrt(x)}log_{7}^{x} - Igx\right)}{dx}\\=&-sin(x) + ({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x} + {\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))}) - Ig\\=&-sin(x) + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})}{2x^{\frac{1}{2}}} - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)}{x} + \frac{{\frac{1}{x}}^{sqrt(x)}}{xln(7)} - Ig\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -sin(x) + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})}{2x^{\frac{1}{2}}} - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)}{x} + \frac{{\frac{1}{x}}^{sqrt(x)}}{xln(7)} - Ig\right)}{dx}\\=&-cos(x) + \frac{\frac{-1}{2}{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})}{2x^{\frac{3}{2}}} + \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}ln(\frac{1}{x})}{2x^{\frac{1}{2}}} + \frac{{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})ln(\frac{1}{x})}{2x^{\frac{1}{2}}} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*-1}{2x^{\frac{1}{2}}(\frac{1}{x})x^{2}} - \frac{-{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)}{x^{2}} - \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}sqrt(x)}{x} - \frac{{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})sqrt(x)}{x} - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*\frac{1}{2}}{x(x)^{\frac{1}{2}}} + \frac{-{\frac{1}{x}}^{sqrt(x)}}{x^{2}ln(7)} + \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{xln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}*-0}{xln^{2}(7)(7)} + 0\\=&-cos(x) - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})sqrt(x)}{x^{\frac{3}{2}}} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{2}(\frac{1}{x})}{4x} - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})}{4x^{\frac{3}{2}}} + \frac{{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{2x^{\frac{3}{2}}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)}{x^{2}} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)^{2}}{x^{2}} - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}}{x^{\frac{3}{2}}} - \frac{2{\frac{1}{x}}^{sqrt(x)}sqrt(x)}{x^{2}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{2x^{\frac{3}{2}}ln(7)} - \frac{{\frac{1}{x}}^{sqrt(x)}}{x^{2}ln(7)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -cos(x) - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})sqrt(x)}{x^{\frac{3}{2}}} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{2}(\frac{1}{x})}{4x} - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})}{4x^{\frac{3}{2}}} + \frac{{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{2x^{\frac{3}{2}}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)}{x^{2}} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)^{2}}{x^{2}} - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}}{x^{\frac{3}{2}}} - \frac{2{\frac{1}{x}}^{sqrt(x)}sqrt(x)}{x^{2}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{2x^{\frac{3}{2}}ln(7)} - \frac{{\frac{1}{x}}^{sqrt(x)}}{x^{2}ln(7)}\right)}{dx}\\=&--sin(x) - \frac{\frac{-3}{2}{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})sqrt(x)}{x^{\frac{5}{2}}} - \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}ln(\frac{1}{x})sqrt(x)}{x^{\frac{3}{2}}} - \frac{{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})ln(\frac{1}{x})sqrt(x)}{x^{\frac{3}{2}}} - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*-sqrt(x)}{x^{\frac{3}{2}}(\frac{1}{x})x^{2}} - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})*\frac{1}{2}}{x^{\frac{3}{2}}(x)^{\frac{1}{2}}} + \frac{-{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{2}(\frac{1}{x})}{4x^{2}} + \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}ln^{2}(\frac{1}{x})}{4x} + \frac{{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})ln^{2}(\frac{1}{x})}{4x} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*2ln(\frac{1}{x})*-1}{4x(\frac{1}{x})x^{2}} - \frac{\frac{-3}{2}{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})}{4x^{\frac{5}{2}}} - \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}ln(\frac{1}{x})}{4x^{\frac{3}{2}}} - \frac{{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})ln(\frac{1}{x})}{4x^{\frac{3}{2}}} - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*-1}{4x^{\frac{3}{2}}(\frac{1}{x})x^{2}} + \frac{\frac{-3}{2}{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{2x^{\frac{5}{2}}ln(7)} + \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(\frac{1}{x})}{2x^{\frac{3}{2}}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}*-0ln(\frac{1}{x})}{2x^{\frac{3}{2}}ln^{2}(7)(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}*-1}{2x^{\frac{3}{2}}ln(7)(\frac{1}{x})x^{2}} + \frac{-2{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)}{x^{3}} + \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}sqrt(x)}{x^{2}} + \frac{{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})sqrt(x)}{x^{2}} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*\frac{1}{2}}{x^{2}(x)^{\frac{1}{2}}} + \frac{-2{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)^{2}}{x^{3}} + \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}sqrt(x)^{2}}{x^{2}} + \frac{{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})sqrt(x)^{2}}{x^{2}} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*2(x)^{\frac{1}{2}}*\frac{1}{2}}{x^{2}(x)^{\frac{1}{2}}} - \frac{\frac{-3}{2}{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}}{x^{\frac{5}{2}}} - \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}}{x^{\frac{3}{2}}} - \frac{{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})}{x^{\frac{3}{2}}} - \frac{2*-2{\frac{1}{x}}^{sqrt(x)}sqrt(x)}{x^{3}ln(7)} - \frac{2({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))sqrt(x)}{x^{2}ln(7)} - \frac{2{\frac{1}{x}}^{sqrt(x)}*-0sqrt(x)}{x^{2}ln^{2}(7)(7)} - \frac{2{\frac{1}{x}}^{sqrt(x)}*\frac{1}{2}}{x^{2}ln(7)(x)^{\frac{1}{2}}} + \frac{\frac{-3}{2}{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{2x^{\frac{5}{2}}ln(7)} + \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(\frac{1}{x})}{2x^{\frac{3}{2}}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}*-1}{2x^{\frac{3}{2}}(\frac{1}{x})x^{2}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})*-0}{2x^{\frac{3}{2}}ln^{2}(7)(7)} - \frac{-2{\frac{1}{x}}^{sqrt(x)}}{x^{3}ln(7)} - \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{x^{2}ln(7)} - \frac{{\frac{1}{x}}^{sqrt(x)}*-0}{x^{2}ln^{2}(7)(7)}\\=&sin(x) + \frac{9{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})sqrt(x)}{4x^{\frac{5}{2}}} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{2}(\frac{1}{x})sqrt(x)}{4x^{2}} + \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})sqrt(x)^{2}}{2x^{\frac{5}{2}}} - \frac{3{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})sqrt(x)}{2x^{\frac{5}{2}}ln(7)} + \frac{2{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)}{x^{\frac{5}{2}}} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})}{2x^{2}} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{2}(\frac{1}{x})}{8x^{2}} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{3}(\frac{1}{x})}{8x^{\frac{3}{2}}} + \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})}{8x^{\frac{5}{2}}} - \frac{3{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})sqrt(x)}{2x^{\frac{5}{2}}ln(7)} - \frac{2{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)}{x^{3}} - \frac{{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{x^{\frac{5}{2}}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}ln^{2}(\frac{1}{x})}{2x^{2}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}ln^{2}(\frac{1}{x})}{4x^{2}ln(7)} + \frac{6{\frac{1}{x}}^{sqrt(x)}sqrt(x)}{x^{3}ln(7)} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)^{2}}{x^{3}} + \frac{3{\frac{1}{x}}^{sqrt(x)}sqrt(x)^{2}}{x^{3}ln(7)} - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)^{3}}{x^{3}} + \frac{9{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}}{4x^{\frac{5}{2}}} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}}{x^{2}} - \frac{5{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{4x^{\frac{5}{2}}ln(7)} - \frac{3{\frac{1}{x}}^{sqrt(x)}}{x^{\frac{5}{2}}ln(7)} + \frac{2{\frac{1}{x}}^{sqrt(x)}}{x^{3}ln(7)}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( sin(x) + \frac{9{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})sqrt(x)}{4x^{\frac{5}{2}}} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{2}(\frac{1}{x})sqrt(x)}{4x^{2}} + \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})sqrt(x)^{2}}{2x^{\frac{5}{2}}} - \frac{3{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})sqrt(x)}{2x^{\frac{5}{2}}ln(7)} + \frac{2{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)}{x^{\frac{5}{2}}} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})}{2x^{2}} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{2}(\frac{1}{x})}{8x^{2}} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{3}(\frac{1}{x})}{8x^{\frac{3}{2}}} + \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})}{8x^{\frac{5}{2}}} - \frac{3{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})sqrt(x)}{2x^{\frac{5}{2}}ln(7)} - \frac{2{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)}{x^{3}} - \frac{{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{x^{\frac{5}{2}}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}ln^{2}(\frac{1}{x})}{2x^{2}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}ln^{2}(\frac{1}{x})}{4x^{2}ln(7)} + \frac{6{\frac{1}{x}}^{sqrt(x)}sqrt(x)}{x^{3}ln(7)} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)^{2}}{x^{3}} + \frac{3{\frac{1}{x}}^{sqrt(x)}sqrt(x)^{2}}{x^{3}ln(7)} - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)^{3}}{x^{3}} + \frac{9{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}}{4x^{\frac{5}{2}}} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}}{x^{2}} - \frac{5{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{4x^{\frac{5}{2}}ln(7)} - \frac{3{\frac{1}{x}}^{sqrt(x)}}{x^{\frac{5}{2}}ln(7)} + \frac{2{\frac{1}{x}}^{sqrt(x)}}{x^{3}ln(7)}\right)}{dx}\\=&cos(x) + \frac{9*\frac{-5}{2}{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})sqrt(x)}{4x^{\frac{7}{2}}} + \frac{9({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}ln(\frac{1}{x})sqrt(x)}{4x^{\frac{5}{2}}} + \frac{9{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})ln(\frac{1}{x})sqrt(x)}{4x^{\frac{5}{2}}} + \frac{9{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*-sqrt(x)}{4x^{\frac{5}{2}}(\frac{1}{x})x^{2}} + \frac{9{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})*\frac{1}{2}}{4x^{\frac{5}{2}}(x)^{\frac{1}{2}}} - \frac{3*-2{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{2}(\frac{1}{x})sqrt(x)}{4x^{3}} - \frac{3({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}ln^{2}(\frac{1}{x})sqrt(x)}{4x^{2}} - \frac{3{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})ln^{2}(\frac{1}{x})sqrt(x)}{4x^{2}} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*2ln(\frac{1}{x})*-sqrt(x)}{4x^{2}(\frac{1}{x})x^{2}} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{2}(\frac{1}{x})*\frac{1}{2}}{4x^{2}(x)^{\frac{1}{2}}} + \frac{3*\frac{-5}{2}{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})sqrt(x)^{2}}{2x^{\frac{7}{2}}} + \frac{3({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}ln(\frac{1}{x})sqrt(x)^{2}}{2x^{\frac{5}{2}}} + \frac{3{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})ln(\frac{1}{x})sqrt(x)^{2}}{2x^{\frac{5}{2}}} + \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*-sqrt(x)^{2}}{2x^{\frac{5}{2}}(\frac{1}{x})x^{2}} + \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})*2(x)^{\frac{1}{2}}*\frac{1}{2}}{2x^{\frac{5}{2}}(x)^{\frac{1}{2}}} - \frac{3*\frac{-5}{2}{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})sqrt(x)}{2x^{\frac{7}{2}}ln(7)} - \frac{3({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(\frac{1}{x})sqrt(x)}{2x^{\frac{5}{2}}ln(7)} - \frac{3{\frac{1}{x}}^{sqrt(x)}*-0ln(\frac{1}{x})sqrt(x)}{2x^{\frac{5}{2}}ln^{2}(7)(7)} - \frac{3{\frac{1}{x}}^{sqrt(x)}*-sqrt(x)}{2x^{\frac{5}{2}}ln(7)(\frac{1}{x})x^{2}} - \frac{3{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})*\frac{1}{2}}{2x^{\frac{5}{2}}ln(7)(x)^{\frac{1}{2}}} + \frac{2*\frac{-5}{2}{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)}{x^{\frac{7}{2}}} + \frac{2({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}sqrt(x)}{x^{\frac{5}{2}}} + \frac{2{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})sqrt(x)}{x^{\frac{5}{2}}} + \frac{2{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*\frac{1}{2}}{x^{\frac{5}{2}}(x)^{\frac{1}{2}}} - \frac{3*-2{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})}{2x^{3}} - \frac{3({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}ln(\frac{1}{x})}{2x^{2}} - \frac{3{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})ln(\frac{1}{x})}{2x^{2}} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*-1}{2x^{2}(\frac{1}{x})x^{2}} - \frac{3*-2{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{2}(\frac{1}{x})}{8x^{3}} - \frac{3({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}ln^{2}(\frac{1}{x})}{8x^{2}} - \frac{3{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})ln^{2}(\frac{1}{x})}{8x^{2}} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*2ln(\frac{1}{x})*-1}{8x^{2}(\frac{1}{x})x^{2}} + \frac{\frac{-3}{2}{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{3}(\frac{1}{x})}{8x^{\frac{5}{2}}} + \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}ln^{3}(\frac{1}{x})}{8x^{\frac{3}{2}}} + \frac{{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})ln^{3}(\frac{1}{x})}{8x^{\frac{3}{2}}} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*3ln^{2}(\frac{1}{x})*-1}{8x^{\frac{3}{2}}(\frac{1}{x})x^{2}} + \frac{3*\frac{-5}{2}{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})}{8x^{\frac{7}{2}}} + \frac{3({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}ln(\frac{1}{x})}{8x^{\frac{5}{2}}} + \frac{3{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})ln(\frac{1}{x})}{8x^{\frac{5}{2}}} + \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*-1}{8x^{\frac{5}{2}}(\frac{1}{x})x^{2}} - \frac{3*\frac{-5}{2}{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})sqrt(x)}{2x^{\frac{7}{2}}ln(7)} - \frac{3({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(\frac{1}{x})sqrt(x)}{2x^{\frac{5}{2}}ln(7)} - \frac{3{\frac{1}{x}}^{sqrt(x)}*-sqrt(x)}{2x^{\frac{5}{2}}(\frac{1}{x})x^{2}ln(7)} - \frac{3{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})*-0sqrt(x)}{2x^{\frac{5}{2}}ln^{2}(7)(7)} - \frac{3{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})*\frac{1}{2}}{2x^{\frac{5}{2}}ln(7)(x)^{\frac{1}{2}}} - \frac{2*-3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)}{x^{4}} - \frac{2({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}sqrt(x)}{x^{3}} - \frac{2{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})sqrt(x)}{x^{3}} - \frac{2{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*\frac{1}{2}}{x^{3}(x)^{\frac{1}{2}}} - \frac{\frac{-5}{2}{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{x^{\frac{7}{2}}ln(7)} - \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(\frac{1}{x})}{x^{\frac{5}{2}}ln(7)} - \frac{{\frac{1}{x}}^{sqrt(x)}*-0ln(\frac{1}{x})}{x^{\frac{5}{2}}ln^{2}(7)(7)} - \frac{{\frac{1}{x}}^{sqrt(x)}*-1}{x^{\frac{5}{2}}ln(7)(\frac{1}{x})x^{2}} + \frac{-2{\frac{1}{x}}^{sqrt(x)}ln^{2}(\frac{1}{x})}{2x^{3}ln(7)} + \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln^{2}(\frac{1}{x})}{2x^{2}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}*2ln(\frac{1}{x})*-1}{2x^{2}(\frac{1}{x})x^{2}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}ln^{2}(\frac{1}{x})*-0}{2x^{2}ln^{2}(7)(7)} + \frac{-2{\frac{1}{x}}^{sqrt(x)}ln^{2}(\frac{1}{x})}{4x^{3}ln(7)} + \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln^{2}(\frac{1}{x})}{4x^{2}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}*-0ln^{2}(\frac{1}{x})}{4x^{2}ln^{2}(7)(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}*2ln(\frac{1}{x})*-1}{4x^{2}ln(7)(\frac{1}{x})x^{2}} + \frac{6*-3{\frac{1}{x}}^{sqrt(x)}sqrt(x)}{x^{4}ln(7)} + \frac{6({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))sqrt(x)}{x^{3}ln(7)} + \frac{6{\frac{1}{x}}^{sqrt(x)}*-0sqrt(x)}{x^{3}ln^{2}(7)(7)} + \frac{6{\frac{1}{x}}^{sqrt(x)}*\frac{1}{2}}{x^{3}ln(7)(x)^{\frac{1}{2}}} - \frac{3*-3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)^{2}}{x^{4}} - \frac{3({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}sqrt(x)^{2}}{x^{3}} - \frac{3{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})sqrt(x)^{2}}{x^{3}} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*2(x)^{\frac{1}{2}}*\frac{1}{2}}{x^{3}(x)^{\frac{1}{2}}} + \frac{3*-3{\frac{1}{x}}^{sqrt(x)}sqrt(x)^{2}}{x^{4}ln(7)} + \frac{3({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))sqrt(x)^{2}}{x^{3}ln(7)} + \frac{3{\frac{1}{x}}^{sqrt(x)}*-0sqrt(x)^{2}}{x^{3}ln^{2}(7)(7)} + \frac{3{\frac{1}{x}}^{sqrt(x)}*2(x)^{\frac{1}{2}}*\frac{1}{2}}{x^{3}ln(7)(x)^{\frac{1}{2}}} - \frac{-3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)^{3}}{x^{4}} - \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}sqrt(x)^{3}}{x^{3}} - \frac{{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})sqrt(x)^{3}}{x^{3}} - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}*3(x)*\frac{1}{2}}{x^{3}(x)^{\frac{1}{2}}} + \frac{9*\frac{-5}{2}{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}}{4x^{\frac{7}{2}}} + \frac{9({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}}{4x^{\frac{5}{2}}} + \frac{9{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})}{4x^{\frac{5}{2}}} + \frac{-2{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}}{x^{3}} + \frac{({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))log_{7}^{x}}{x^{2}} + \frac{{\frac{1}{x}}^{sqrt(x)}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{7}^{x}}{(7)})}{(ln(7))})}{x^{2}} - \frac{5*\frac{-5}{2}{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{4x^{\frac{7}{2}}ln(7)} - \frac{5({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))ln(\frac{1}{x})}{4x^{\frac{5}{2}}ln(7)} - \frac{5{\frac{1}{x}}^{sqrt(x)}*-1}{4x^{\frac{5}{2}}(\frac{1}{x})x^{2}ln(7)} - \frac{5{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})*-0}{4x^{\frac{5}{2}}ln^{2}(7)(7)} - \frac{3*\frac{-5}{2}{\frac{1}{x}}^{sqrt(x)}}{x^{\frac{7}{2}}ln(7)} - \frac{3({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{x^{\frac{5}{2}}ln(7)} - \frac{3{\frac{1}{x}}^{sqrt(x)}*-0}{x^{\frac{5}{2}}ln^{2}(7)(7)} + \frac{2*-3{\frac{1}{x}}^{sqrt(x)}}{x^{4}ln(7)} + \frac{2({\frac{1}{x}}^{sqrt(x)}((\frac{\frac{1}{2}}{(x)^{\frac{1}{2}}})ln(\frac{1}{x}) + \frac{(sqrt(x))(\frac{-1}{x^{2}})}{(\frac{1}{x})}))}{x^{3}ln(7)} + \frac{2{\frac{1}{x}}^{sqrt(x)}*-0}{x^{3}ln^{2}(7)(7)}\\=&cos(x) - \frac{7{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})sqrt(x)}{x^{\frac{7}{2}}} + \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{2}(\frac{1}{x})sqrt(x)}{x^{3}} - \frac{15{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})sqrt(x)^{2}}{2x^{\frac{7}{2}}} + \frac{3{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})sqrt(x)^{2}}{x^{\frac{7}{2}}ln(7)} - \frac{19{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)}{2x^{\frac{7}{2}}} - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{3}(\frac{1}{x})sqrt(x)}{2x^{\frac{5}{2}}} + \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{2}(\frac{1}{x})sqrt(x)^{2}}{2x^{3}} + \frac{4{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})sqrt(x)}{x^{3}} + \frac{3{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})sqrt(x)^{2}}{x^{\frac{7}{2}}ln(7)} - \frac{2{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})sqrt(x)^{3}}{x^{\frac{7}{2}}} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{2}(\frac{1}{x})}{2x^{\frac{5}{2}}} + \frac{6{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})}{x^{3}} - \frac{7{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)^{2}}{2x^{\frac{7}{2}}} + \frac{2{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})}{x^{\frac{5}{2}}} + \frac{7{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})sqrt(x)}{x^{\frac{7}{2}}ln(7)} - \frac{2{\frac{1}{x}}^{sqrt(x)}ln^{2}(\frac{1}{x})sqrt(x)}{x^{3}ln(7)} + \frac{8{\frac{1}{x}}^{sqrt(x)}sqrt(x)}{x^{\frac{7}{2}}ln(7)} - \frac{{\frac{1}{x}}^{sqrt(x)}ln^{2}(\frac{1}{x})sqrt(x)}{x^{3}ln(7)} - \frac{18{\frac{1}{x}}^{sqrt(x)}sqrt(x)^{2}}{x^{4}ln(7)} + \frac{15{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{2}(\frac{1}{x})}{16x^{3}} + \frac{8{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})sqrt(x)}{x^{\frac{7}{2}}ln(7)} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{3}(\frac{1}{x})}{8x^{\frac{5}{2}}} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln^{4}(\frac{1}{x})}{16x^{2}} - \frac{15{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}ln(\frac{1}{x})}{16x^{\frac{7}{2}}} + \frac{6{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)}{x^{4}} + \frac{11{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)^{2}}{x^{4}} + \frac{6{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)^{3}}{x^{4}} - \frac{9{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{4x^{3}ln(7)} - \frac{15{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{4x^{3}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)^{4}}{x^{4}} - \frac{4{\frac{1}{x}}^{sqrt(x)}sqrt(x)^{3}}{x^{4}ln(7)} - \frac{{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}sqrt(x)}{x^{3}} + \frac{23{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{8x^{\frac{7}{2}}ln(7)} - \frac{17{\frac{1}{x}}^{sqrt(x)}ln^{2}(\frac{1}{x})}{8x^{3}ln(7)} - \frac{7{\frac{1}{x}}^{sqrt(x)}ln^{2}(\frac{1}{x})}{8x^{3}ln(7)} + \frac{3{\frac{1}{x}}^{sqrt(x)}ln^{3}(\frac{1}{x})}{8x^{\frac{5}{2}}ln(7)} + \frac{{\frac{1}{x}}^{sqrt(x)}ln^{3}(\frac{1}{x})}{8x^{\frac{5}{2}}ln(7)} - \frac{22{\frac{1}{x}}^{sqrt(x)}sqrt(x)}{x^{4}ln(7)} + \frac{33{\frac{1}{x}}^{sqrt(x)}ln(\frac{1}{x})}{8x^{\frac{7}{2}}ln(7)} + \frac{4{\frac{1}{x}}^{sqrt(x)}}{x^{3}ln(7)} - \frac{5{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}}{2x^{3}} - \frac{3{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}}{2x^{\frac{5}{2}}} - \frac{7{\frac{1}{x}}^{sqrt(x)}log_{7}^{x}}{x^{\frac{7}{2}}} + \frac{15{\frac{1}{x}}^{sqrt(x)}}{x^{\frac{7}{2}}ln(7)} - \frac{6{\frac{1}{x}}^{sqrt(x)}}{x^{4}ln(7)}\\ \end{split}\end{equation}