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