There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (3{x}^{2} + 2{(({x}^{3} + 4){\frac{1}{x}}^{4})}^{\frac{1}{2}}){\frac{1}{(({x}^{3} - 4)({x}^{2} + 2))}}^{\frac{1}{2}}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{3x^{2}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} + \frac{2(x^{3} + 4)^{\frac{1}{2}}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}x^{2}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{3x^{2}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} + \frac{2(x^{3} + 4)^{\frac{1}{2}}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}x^{2}}\right)}{dx}\\=&3(\frac{\frac{-1}{2}(5x^{4} + 2*3x^{2} - 4*2x + 0)}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}})x^{2} + \frac{3*2x}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} + \frac{2(\frac{\frac{1}{2}(3x^{2} + 0)}{(x^{3} + 4)^{\frac{1}{2}}})}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}x^{2}} + \frac{2(x^{3} + 4)^{\frac{1}{2}}(\frac{\frac{-1}{2}(5x^{4} + 2*3x^{2} - 4*2x + 0)}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}})}{x^{2}} + \frac{2(x^{3} + 4)^{\frac{1}{2}}*-2}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}x^{3}}\\=&\frac{-15x^{6}}{2(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}} - \frac{9x^{4}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}} + \frac{12x^{3}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}} + \frac{6x}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} - \frac{4(x^{3} + 4)^{\frac{1}{2}}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}x^{3}} - \frac{5(x^{3} + 4)^{\frac{1}{2}}x^{2}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}} + \frac{8(x^{3} + 4)^{\frac{1}{2}}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}x} - \frac{6(x^{3} + 4)^{\frac{1}{2}}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}} + \frac{3}{(x^{3} + 4)^{\frac{1}{2}}(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!