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

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