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

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