Module 11 :   Partial derivatives, Chain rules,  Implicit differentiation, Gradient, Directional derivatives
Lecture 31 :  Partial derivatives  [Section 31.1]
  if it exists.
31.1.3 Examples:
(1)

Let be given by

 

Then, both the partial derivatives of exists at every . In fact,

These are obtained by differentiating the functions of one variables and
, respectively.

(2)
 Let be given by
 

For we have

At , since


clearly does not exist. Similarly, does not exist.

1
4