Jacobians of functions with variables constraints

Question

Consider a function $f(a,b)$, where $a,b\in \mathbb{R}^n$ with $n>1$. The variables are also subject to a function $g(a,b)=0\in \mathbb{R}^m, m<n$. Is there any guidelines to calculate the Jacobians $\frac{\partial f(\cdot)}{\partial a}$ and $\frac{\partial f(\cdots)}{\partial b}$ ?