4e. Find the first and second derivative.
We first rewrite
and use the quotient rule.
This is often written
For the second derivative, let us rewrite the first derivative as
and use the power rule. Move the power in front of the parentheses, and raise the quantity inside the parentheses to one smaller power, and multiply everything by the derivative of the inside function.
This can be cleaned up to
which can also be written as