There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (3{x}^{2} + 2{({x}^{3} + 4{\frac{1}{x}}^{4})}^{\frac{1}{2}}){\frac{1}{(({x}^{3} - 4)({x}^{2} + 2))}}^{\frac{1}{2}}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{3x^{2}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} + \frac{2(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{3x^{2}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} + \frac{2(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}}\right)}{dx}\\=&3(\frac{\frac{-1}{2}(5x^{4} + 2*3x^{2} - 4*2x + 0)}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}})x^{2} + \frac{3*2x}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} + \frac{2(\frac{\frac{1}{2}(3x^{2} + \frac{4*-4}{x^{5}})}{(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}})}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} + 2(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}(\frac{\frac{-1}{2}(5x^{4} + 2*3x^{2} - 4*2x + 0)}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}})\\=&\frac{-15x^{6}}{2(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}} - \frac{9x^{4}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}} + \frac{12x^{3}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}} + \frac{6x}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} + \frac{3x^{2}}{(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}} - \frac{16}{(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{1}{2}}x^{5}} - \frac{5(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}x^{4}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}} - \frac{6(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}x^{2}}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}} + \frac{8(x^{3} + \frac{4}{x^{4}})^{\frac{1}{2}}x}{(x^{5} + 2x^{3} - 4x^{2} - 8)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]Your problem has not been solved here? Please go to the Hot Problems section!