Mathematics
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current location:Derivative function > Derivative function calculation history > Answer
    There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{x{e}^{(3x)}}{3} + 19sin(x) + 17xarctan(8)\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{3}x{e}^{(3x)} + 19sin(x) + 17xarctan(8)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{1}{3}x{e}^{(3x)} + 19sin(x) + 17xarctan(8)\right)}{dx}\\=&\frac{1}{3}{e}^{(3x)} + \frac{1}{3}x({e}^{(3x)}((3)ln(e) + \frac{(3x)(0)}{(e)})) + 19cos(x) + 17arctan(8) + 17x(\frac{(0)}{(1 + (8)^{2})})\\=&\frac{{e}^{(3x)}}{3} + x{e}^{(3x)} + 19cos(x) + 17arctan(8)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{{e}^{(3x)}}{3} + x{e}^{(3x)} + 19cos(x) + 17arctan(8)\right)}{dx}\\=&\frac{({e}^{(3x)}((3)ln(e) + \frac{(3x)(0)}{(e)}))}{3} + {e}^{(3x)} + x({e}^{(3x)}((3)ln(e) + \frac{(3x)(0)}{(e)})) + 19*-sin(x) + 17(\frac{(0)}{(1 + (8)^{2})})\\=&2{e}^{(3x)} + 3x{e}^{(3x)} - 19sin(x)\\ \end{split}\end{equation} \]





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