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Sunday, February 16, 2014

Implicit Differentiation, 7

Category: Differential Calculus, Algebra

"Published in Vacaville, California, USA"

Find dy/dx and d2y/dx2 by implicit differentiation for:


Solution:

Consider the given equation above


Take the first derivative of the given equation with respect to x by implicit differentiation, we have







Finally, take the second derivative of the above equation with respect to x by implicit differentiation, we have








but



Hence, the above equation becomes
 
 
 
 
 
   
We can further simplify the above equation by using the given equation as follows
 
 
  Therefore,