Let $T(X)$ be an efficient estimator (its variance equates the Cramer-Rao bound) of the parameter $\theta$. A theorem in my course states that it is the only maximum likelihood estimator of $\theta$.   

The proof states that : 
$$ \frac{\partial p(x,\theta)}{\partial \theta} = I\_{X}(\theta)\big[T(X) - \theta \big] $$
and the partial derivative is $0$ if $T(X) = \theta$, but where does this partial derivative come from?