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

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