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

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