Module 11 :   Partial derivatives, Chain rules,  Implicit differentiation, Gradient, Directional derivatives
Lecture 32 :  Chain rules [Section 32.1]
32.1.2 Theorem (Chain rule-II):
 

Let and be differentiable at Let and

be functions such that

If exist at then the composite function

has partial derivatives and given by

Symbolically,

32.1.3 Examples:
(i)

Let

 


and

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