Module 11 :   Partial derivatives, Chain rules,  Implicit differentiation, Gradient, Directional derivatives
Lecture 31 :  Differentiability [Section 31.2]
31.2.4 Theorem:
 

Let be such that is differentiable at . Then is continuous at .

  Proof
 

Since differentiable at we have

where both as . Thus, we have

Hence, is continuous at .

We describe next a sufficient condition for the differentiability of .

 
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