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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
