There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {x}^{(\frac{2}{3})} + \frac{e{(pi - {x}^{2})}^{\frac{1}{2}}sin(8pix)}{3}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{3}(pi - x^{2})^{\frac{1}{2}}esin(8pix) + x^{\frac{2}{3}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{1}{3}(pi - x^{2})^{\frac{1}{2}}esin(8pix) + x^{\frac{2}{3}}\right)}{dx}\\=&\frac{1}{3}(\frac{\frac{1}{2}(0 - 2x)}{(pi - x^{2})^{\frac{1}{2}}})esin(8pix) + \frac{1}{3}(pi - x^{2})^{\frac{1}{2}}*0sin(8pix) + \frac{1}{3}(pi - x^{2})^{\frac{1}{2}}ecos(8pix)*8pi + \frac{\frac{2}{3}}{x^{\frac{1}{3}}}\\=& - \frac{xesin(8pix)}{3(pi - x^{2})^{\frac{1}{2}}} + \frac{8(pi - x^{2})^{\frac{1}{2}}piecos(8pix)}{3} + \frac{2}{3x^{\frac{1}{3}}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please take a look at the hot problems !