# 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?

-

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

-
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

We can find the derivative of the activation function in the book "Introduction to artificial neural systems" and the author is named "WESTJACEK M. ZURADA", Professor of Electrical Engineering and of Computer Science and Engineering good luck

-