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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,