There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (1 + sqrt(5d){\frac{1}{10}}^{x} + \frac{5{d}^{2}}{(3 * {10}^{2}x)}){e}^{(sqrt(5)d{\frac{1}{10}}^{x})}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {\frac{1}{10}}^{x}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}sqrt(5d) + {e}^{(d{\frac{1}{10}}^{x}sqrt(5))} + \frac{\frac{1}{60}d^{2}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}}{x}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( {\frac{1}{10}}^{x}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}sqrt(5d) + {e}^{(d{\frac{1}{10}}^{x}sqrt(5))} + \frac{\frac{1}{60}d^{2}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}}{x}\right)}{dx}\\=&({\frac{1}{10}}^{x}((1)ln(\frac{1}{10}) + \frac{(x)(0)}{(\frac{1}{10})})){e}^{(d{\frac{1}{10}}^{x}sqrt(5))}sqrt(5d) + {\frac{1}{10}}^{x}({e}^{(d{\frac{1}{10}}^{x}sqrt(5))}((d({\frac{1}{10}}^{x}((1)ln(\frac{1}{10}) + \frac{(x)(0)}{(\frac{1}{10})}))sqrt(5) + d{\frac{1}{10}}^{x}*0*\frac{1}{2}*5^{\frac{1}{2}})ln(e) + \frac{(d{\frac{1}{10}}^{x}sqrt(5))(0)}{(e)}))sqrt(5d) + \frac{{\frac{1}{10}}^{x}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}*0*\frac{1}{2}}{(5d)^{\frac{1}{2}}} + ({e}^{(d{\frac{1}{10}}^{x}sqrt(5))}((d({\frac{1}{10}}^{x}((1)ln(\frac{1}{10}) + \frac{(x)(0)}{(\frac{1}{10})}))sqrt(5) + d{\frac{1}{10}}^{x}*0*\frac{1}{2}*5^{\frac{1}{2}})ln(e) + \frac{(d{\frac{1}{10}}^{x}sqrt(5))(0)}{(e)})) + \frac{\frac{1}{60}d^{2}*-{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}}{x^{2}} + \frac{\frac{1}{60}d^{2}({e}^{(d{\frac{1}{10}}^{x}sqrt(5))}((d({\frac{1}{10}}^{x}((1)ln(\frac{1}{10}) + \frac{(x)(0)}{(\frac{1}{10})}))sqrt(5) + d{\frac{1}{10}}^{x}*0*\frac{1}{2}*5^{\frac{1}{2}})ln(e) + \frac{(d{\frac{1}{10}}^{x}sqrt(5))(0)}{(e)}))}{x}\\=&{\frac{1}{10}}^{x}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}ln(\frac{1}{10})sqrt(5d) + d{\frac{1}{10}}^{(2x)}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}ln(\frac{1}{10})sqrt(5)sqrt(5d) + d{\frac{1}{10}}^{x}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}ln(\frac{1}{10})sqrt(5) + \frac{d^{3}{\frac{1}{10}}^{x}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}ln(\frac{1}{10})sqrt(5)}{60x} - \frac{d^{2}{e}^{(d{\frac{1}{10}}^{x}sqrt(5))}}{60x^{2}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!