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

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