# Show the derivative of an activation function

I am learning about neural networks and am using the sigmoid activation function

$$q(z)=\frac{1}{1+e^{-z}}.$$ The problem is that I need to use its derivative $q^{\prime}(z)$. Would anyone have any hints as to how I would go about calculating this?

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## 1 Answer

Hint: $$\left(\frac 1f\right)^{\prime}=-\frac{f^{\prime}}{f^2}$$ when $f$ is non zero and differentiable. This means $$q^{\prime}(z)=\left(\frac{1}{1+e^{-z}}\right)^{\prime}=-\frac{(1+e^{-z})^{\prime}}{(1+e^{-z})^2}$$

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Mhh, sorry, I don't quite get it...one more hint? :) Is it just q'(z) = q(z)^2 ? – user1796218 Dec 27 '12 at 12:19
Ahh, ok, that makes sense. Thank you!!  So, q'(z) = q(z)(1-q(z)). – user1796218 Dec 27 '12 at 12:35
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