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