There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {sqrt(((\frac{1}{4})x + sqrt(48 - (\frac{15}{16}){x}^{2})) - x)}^{2} + (\frac{3}{4}){x}^{2}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(\frac{-3}{4}x + sqrt(\frac{-15}{16}x^{2} + 48))^{2} + \frac{3}{4}x^{2}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( sqrt(\frac{-3}{4}x + sqrt(\frac{-15}{16}x^{2} + 48))^{2} + \frac{3}{4}x^{2}\right)}{dx}\\=&\frac{2(\frac{-3}{4}x + sqrt(\frac{-15}{16}x^{2} + 48))^{\frac{1}{2}}(\frac{-3}{4} + \frac{(\frac{-15}{16}*2x + 0)*\frac{1}{2}}{(\frac{-15}{16}x^{2} + 48)^{\frac{1}{2}}})*\frac{1}{2}}{(\frac{-3}{4}x + sqrt(\frac{-15}{16}x^{2} + 48))^{\frac{1}{2}}} + \frac{3}{4}*2x\\=&\frac{-15x}{16(\frac{-15}{16}x^{2} + 48)^{\frac{1}{2}}} + \frac{3x}{2} - \frac{3}{4}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!