There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt({(x + 1)}^{10}{\frac{1}{(2x + 1)}}^{5})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = sqrt(\frac{(x + 1)^{10}}{(2x + 1)^{5}})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( sqrt(\frac{(x + 1)^{10}}{(2x + 1)^{5}})\right)}{dx}\\=&\frac{(\frac{(10(x + 1)^{9}(1 + 0))}{(2x + 1)^{5}} + (x + 1)^{10}(\frac{-5(2 + 0)}{(2x + 1)^{6}}))*\frac{1}{2}}{(\frac{(x + 1)^{10}}{(2x + 1)^{5}})^{\frac{1}{2}}}\\=&\frac{5x^{4}}{(2x + 1)^{\frac{5}{2}}} + \frac{20x^{3}}{(2x + 1)^{\frac{5}{2}}} + \frac{30x^{2}}{(2x + 1)^{\frac{5}{2}}} + \frac{20x}{(2x + 1)^{\frac{5}{2}}} - \frac{5x^{5}}{(2x + 1)^{\frac{7}{2}}} - \frac{25x^{4}}{(2x + 1)^{\frac{7}{2}}} - \frac{50x^{3}}{(2x + 1)^{\frac{7}{2}}} - \frac{50x^{2}}{(2x + 1)^{\frac{7}{2}}} - \frac{25x}{(2x + 1)^{\frac{7}{2}}} + \frac{5}{(2x + 1)^{\frac{5}{2}}} - \frac{5}{(2x + 1)^{\frac{7}{2}}}\\ \end{split}\end{equation} \]

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