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

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