There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {x}^{2}sqrt(ln({x}^{7} - tan(\frac{1}{(1 - {x}^{(x - {\frac{1}{x}}^{5})})})) + 1)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{2}sqrt(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( x^{2}sqrt(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)\right)}{dx}\\=&2xsqrt(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1) + \frac{x^{2}(\frac{(7x^{6} - sec^{2}(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})((\frac{-(-({x}^{(x - \frac{1}{x^{5}})}((1 - \frac{-5}{x^{6}})ln(x) + \frac{(x - \frac{1}{x^{5}})(1)}{(x)})) + 0)}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)^{2}})))}{(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)}))} + 0)*\frac{1}{2}}{(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)^{\frac{1}{2}}}\\=&2xsqrt(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1) + \frac{7x^{8}}{2(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)}))(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)^{\frac{1}{2}}} - \frac{5{x}^{(x - \frac{1}{x^{5}})}ln(x)sec^{2}(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})}{2(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)}))(-{x}^{(x - \frac{1}{x^{5}})} + 1)^{2}(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)^{\frac{1}{2}}x^{4}} - \frac{x^{2}{x}^{(x - \frac{1}{x^{5}})}ln(x)sec^{2}(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})}{2(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)}))(-{x}^{(x - \frac{1}{x^{5}})} + 1)^{2}(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)^{\frac{1}{2}}} - \frac{x^{2}{x}^{(x - \frac{1}{x^{5}})}sec^{2}(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})}{2(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)}))(-{x}^{(x - \frac{1}{x^{5}})} + 1)^{2}(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)^{\frac{1}{2}}} + \frac{{x}^{(x - \frac{1}{x^{5}})}sec^{2}(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})}{2(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)}))(-{x}^{(x - \frac{1}{x^{5}})} + 1)^{2}(ln(x^{7} - tan(\frac{1}{(-{x}^{(x - \frac{1}{x^{5}})} + 1)})) + 1)^{\frac{1}{2}}x^{4}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!