Module 11 :   Partial derivatives, Chain rules,  Implicit differentiation, Gradient, Directional derivatives
Lecture 31 :  Partial derivatives  [Section 31.1]
  along two paths, namely the ones parallel to axes. A more general concept of rate of change of function, which takes into account all directions is described in the next section.
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  Practical Exercises
(1)

Examine the following functions for the existence of partial derivatives at . The expressions below give

  the value at . At , the value should be taken as zero:
 

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Answers

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