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

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