What's the derivative of |x+1|(x+2)

How do you find it?

Derivative at what? It is not differentiable at x = -1.

One of the basic differentiation rule is:
Y=UV
Y'=U'V+V'U (' means the derivative of)
Using this,
Y'=1(x+2)+1(x+1)
Y'=x+2+x+1
Y'=2x+3