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 1 derivative of b is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ x{e}^{(-wx - b)}{\frac{1}{({e}^{(-wx - b)} + 1)}}^{2}\ with\ respect\ to\ b:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x{e}^{(-xw - b)}}{({e}^{(-xw - b)} + 1)^{2}}\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( \frac{x{e}^{(-xw - b)}}{({e}^{(-xw - b)} + 1)^{2}}\right)}{db}\\=&(\frac{-2(({e}^{(-xw - b)}((0 - 1)ln(e) + \frac{(-xw - b)(0)}{(e)})) + 0)}{({e}^{(-xw - b)} + 1)^{3}})x{e}^{(-xw - b)} + \frac{x({e}^{(-xw - b)}((0 - 1)ln(e) + \frac{(-xw - b)(0)}{(e)}))}{({e}^{(-xw - b)} + 1)^{2}}\\=&\frac{2x{e}^{(-2xw - 2b)}}{({e}^{(-xw - b)} + 1)^{3}} - \frac{x{e}^{(-xw - b)}}{({e}^{(-xw - b)} + 1)^{2}}\\ \end{split}\end{equation} \]





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