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.

Since your function $$\varphi(v)=\frac{1}{1+e^{-av}}$$
is a function of only one variable (which is $v$), the value of the derivative at the origin is given by setting $v=0$ in your equation for $$\frac{\mathrm{d}\varphi}{\mathrm{d}v}=\frac{a}{1+e^{-av}}\left[1-\frac{1}{1+e^{-av}}\right]=\frac{a}{1+e^{-a\cdot 0}}\left[1-\frac{1}{1+e^{-a\cdot 0}}\right]=\frac{a}{1+1}\left[1-\frac{1}{1+1}\right]=\frac{a}{4}$$ 
