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Monday, December 24, 2012

Partial Differentiation - Three Variables

Category: Differential Calculus

"Published in Newark, California, USA"

If

show that 

Solution:

If you will take the partial derivative of a function with respect to a certain variable, then the other variables will be treated as a constant. Consider the given equation



Take the partial derivative with respect to x, consider y as a constant as follows









Take the partial derivative with respect to y, consider x as a constant as follows









To prove that

Substitute the values of the partial derivative and the value of z to the above equation, we have













Therefore,