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

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