Recall that for a differentiable function of one-variable, if is also a differentiable function of then the composite function is also a differentiable function of and

Similar results hold for functions of several variables.

We state next another such rule, the proof of which is similar to the Chain rule-I, and is left as an exercise.

Let and be differentiable at Let and
               
be functions such that
             
If x, y are both differentiable at then the composite function
             given by
             is differentiable at
and
            

Functionally, this is also written as