There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ lg(4){(x - \frac{4}{x})}^{\frac{1}{2}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x - \frac{4}{x})^{\frac{1}{2}}lg(4)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x - \frac{4}{x})^{\frac{1}{2}}lg(4)\right)}{dx}\\=&(\frac{\frac{1}{2}(1 - \frac{4*-1}{x^{2}})}{(x - \frac{4}{x})^{\frac{1}{2}}})lg(4) + \frac{(x - \frac{4}{x})^{\frac{1}{2}}*0}{ln{10}(4)}\\=&\frac{2lg(4)}{(x - \frac{4}{x})^{\frac{1}{2}}x^{2}} + \frac{lg(4)}{2(x - \frac{4}{x})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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