There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 8sqrt(5)sqrt((4{x}^{2} + x){\frac{1}{(1 + 5x)}}^{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 8sqrt(5)sqrt(\frac{4x^{2}}{(5x + 1)^{2}} + \frac{x}{(5x + 1)^{2}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 8sqrt(5)sqrt(\frac{4x^{2}}{(5x + 1)^{2}} + \frac{x}{(5x + 1)^{2}})\right)}{dx}\\=&8*0*\frac{1}{2}*5^{\frac{1}{2}}sqrt(\frac{4x^{2}}{(5x + 1)^{2}} + \frac{x}{(5x + 1)^{2}}) + \frac{8sqrt(5)(4(\frac{-2(5 + 0)}{(5x + 1)^{3}})x^{2} + \frac{4*2x}{(5x + 1)^{2}} + (\frac{-2(5 + 0)}{(5x + 1)^{3}})x + \frac{1}{(5x + 1)^{2}})*\frac{1}{2}}{(\frac{4x^{2}}{(5x + 1)^{2}} + \frac{x}{(5x + 1)^{2}})^{\frac{1}{2}}}\\=&\frac{-160x^{2}sqrt(5)}{(5x + 1)^{3}(\frac{4x^{2}}{(5x + 1)^{2}} + \frac{x}{(5x + 1)^{2}})^{\frac{1}{2}}} + \frac{32xsqrt(5)}{(5x + 1)^{2}(\frac{4x^{2}}{(5x + 1)^{2}} + \frac{x}{(5x + 1)^{2}})^{\frac{1}{2}}} - \frac{40xsqrt(5)}{(5x + 1)^{3}(\frac{4x^{2}}{(5x + 1)^{2}} + \frac{x}{(5x + 1)^{2}})^{\frac{1}{2}}} + \frac{4sqrt(5)}{(5x + 1)^{2}(\frac{4x^{2}}{(5x + 1)^{2}} + \frac{x}{(5x + 1)^{2}})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！