Calculate the value of a derivative at the origin I have the following question in a course:
An example of the logistic function is defined by
$$\varphi(v)=\frac{1}{1+e^{-av}}$$ 
whose limiting values are $0$ and $1$. Show that the derivative of $\varphi(v)$ with respect to $v$ is given by 
$$\frac{\mathrm{d}\varphi}{\mathrm{d}v}=a\varphi(v)[1-\varphi(v)]$$
What is the value of this derivative at the origin?
The first part is solved, but I couldn't understand the second (What is the value of this derivative at the origin?).
Can anyone help me?
Thanks in advance.

$$\varphi(v)=\frac{1}{1+e^{-av}}\Longrightarrow$$
$$\frac{\partial\varphi(v)}{\partial v}=\frac{\partial}{\partial v}\left(\frac{1}{1+e^{-av}}\right)=\frac{a\cdot e^{av}}{\left(1+e^{av}\right)^2}$$
Now if $v=0$:
$$\varphi'(0)=\frac{a\cdot e^{a\cdot 0}}{\left(1+e^{a\cdot 0}\right)^2}=\frac{a\cdot e^{0}}{\left(1+e^{0}\right)^2}=\frac{a\cdot 1}{(1+1)^2}=\frac{a}{2^2}=\frac{a}{4}$$
