Part 11 (5 points, non-coding task)
Compute
\frac{d \sigma \left( z \right)}{dz} .
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Express your answer using \sigma \left( z \right) only (e^z or e^{-z} should not appear in your final solution).
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Reasoning is required.
\color{green}{\text{### WRITE YOUR SOLUTION HERE ###}}
We have
\begin{align*}
\frac{d \sigma \left( z \right)}{d z}
& = \frac{e^{-z}}{\left( 1 + e^{-z} \right)^2} \\
& = \boxed{ \sigma \left( z \right)
\left( 1 - \sigma \left( z \right) \right) } .
\end{align*}
\color{red}{\text{""" END OF THIS PART """}}