Derivative with respect to a vector of a scalar function that depends on the gradient of the vector

Question

Let $u\in \mathbb{R}^n$ be a vector field, and $f: \mathbb{R}^{n\times n}\to\mathbb{R}$ a differentiable function. Consider the function $f(\nabla u)$ where $\nabla u$ is the gradient of $u$, i.e. $(\nabla u)_{i,j}=\partial u_i/\partial x_j$. In the paper by Miehe, J. Mech. Phys. Solids 59 (2011) eq. (18), it is stated that $$\frac{\partial f}{\partial u}=-{\rm div}\ (\frac{\partial f}{\partial \nabla u})$$ Could please someone tell me how to get this relation? Thanks.