Module 11 :   Partial derivatives, Chain rules,  Implicit differentiation, Gradient, Directional derivatives
Lecture 32 :  Chain rules [Section 32.1]
 

Then, exist everywhere and

Hence, if

then

However, since

we have This does not contradict Chain Rule as is not differentiable (in fact not even continuous ) at

32.1.4 Remark:
 

Chain rule extends to functions of three or more variables as above for functions of two variables.

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