Sorry if this is too simple. This is my first question here.

Suppose $f : R^n \to R$ is a differentiable function. Say that we can compute in $T$ arithmetic operations the value $f(x)$ at any point $x$. Can we use that to somehow precisely bound the time that is required to compute $\nabla f$? (Intuitively because of finite difference approximations, we might be able to do this, but is a precise statement available, or am I overlooking something obvious?)