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

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