There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{-{x}^{2}}{(90000000000000000sqrt(1 - \frac{{x}^{2}}{90000000000000000}))} + sqrt(1 - \frac{{x}^{2}}{90000000000000000})\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{-1}{90000000000000000}x^{2}}{sqrt(\frac{-1}{90000000000000000}x^{2} + 1)} + sqrt(\frac{-1}{90000000000000000}x^{2} + 1)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{\frac{-1}{90000000000000000}x^{2}}{sqrt(\frac{-1}{90000000000000000}x^{2} + 1)} + sqrt(\frac{-1}{90000000000000000}x^{2} + 1)\right)}{dx}\\=&\frac{\frac{-1}{90000000000000000}*2x}{sqrt(\frac{-1}{90000000000000000}x^{2} + 1)} - \frac{\frac{1}{90000000000000000}x^{2}*-(\frac{-1}{90000000000000000}*2x + 0)*\frac{1}{2}}{(\frac{-1}{90000000000000000}x^{2} + 1)(\frac{-1}{90000000000000000}x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{-1}{90000000000000000}*2x + 0)*\frac{1}{2}}{(\frac{-1}{90000000000000000}x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{-x}{45000000000000000sqrt(\frac{-1}{90000000000000000}x^{2} + 1)} - \frac{x^{3}}{5456049174044737536(\frac{-1}{90000000000000000}x^{2} + 1)^{\frac{3}{2}}} - \frac{x}{90000000000000000(\frac{-1}{90000000000000000}x^{2} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!