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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{1}{(1 + 0.792({e}^{(0.136x)}))}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{(0.792{e}^{(0.136x)} + 1)}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{1}{(0.792{e}^{(0.136x)} + 1)}\right)}{dx}\\=&(\frac{-(0.792({e}^{(0.136x)}((0.136)ln(e) + \frac{(0.136x)(0)}{(e)})) + 0)}{(0.792{e}^{(0.136x)} + 1)^{2}})\\=&\frac{-0.107712{e}^{(0.136x)}}{(0.792{e}^{(0.136x)} + 1)(0.792{e}^{(0.136x)} + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-0.107712{e}^{(0.136x)}}{(0.792{e}^{(0.136x)} + 1)(0.792{e}^{(0.136x)} + 1)}\right)}{dx}\\=&\frac{-0.107712(\frac{-(0.792({e}^{(0.136x)}((0.136)ln(e) + \frac{(0.136x)(0)}{(e)})) + 0)}{(0.792{e}^{(0.136x)} + 1)^{2}}){e}^{(0.136x)}}{(0.792{e}^{(0.136x)} + 1)} - \frac{0.107712(\frac{-(0.792({e}^{(0.136x)}((0.136)ln(e) + \frac{(0.136x)(0)}{(e)})) + 0)}{(0.792{e}^{(0.136x)} + 1)^{2}}){e}^{(0.136x)}}{(0.792{e}^{(0.136x)} + 1)} - \frac{0.107712({e}^{(0.136x)}((0.136)ln(e) + \frac{(0.136x)(0)}{(e)}))}{(0.792{e}^{(0.136x)} + 1)(0.792{e}^{(0.136x)} + 1)}\\=&\frac{0.011601874944{e}^{(0.136x)}{e}^{(0.136x)}}{(0.792{e}^{(0.136x)} + 1)(0.792{e}^{(0.136x)} + 1)(0.792{e}^{(0.136x)} + 1)} + \frac{0.011601874944{e}^{(0.136x)}{e}^{(0.136x)}}{(0.792{e}^{(0.136x)} + 1)(0.792{e}^{(0.136x)} + 1)(0.792{e}^{(0.136x)} + 1)} - \frac{0.014648832{e}^{(0.136x)}}{(0.792{e}^{(0.136x)} + 1)(0.792{e}^{(0.136x)} + 1)}\\ \end{split}\end{equation} \]





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