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

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