__Category__: Differential Calculus, Algebra"Published in Newark, California, USA"

Find the derivative for

__Solution__:

Consider the given equation above

The above equation is an exponential function but we cannot take the derivative by exponential function or even by power because the exponent of an algebraic function is also an algebraic function. In this type of exponential function, we need to take natural logarithm on both sides of an equation in order to eliminate the algebraic exponent of an algebraic function.

Take natural logarithm on both sides on an equation, we have

Take the derivative on both sides of the equation with respect to x

Multiply on both sides of the equation by y

but

Hence, the above equation becomes

Therefore, the final answer is