What is the derivative of #sin^2(x) * cos^2(x)#?
By the chain and product rules,
In order to evaluate this derivative, we need to use both the product and chain rules.
Now, by the product rule, we multiply this by our second term,
Now for the right side, we use the chain rule to take the derivative of
Similarly to with the left side, we now multiply this by our
Continuing with the product rule, we add the left- and right-hand derivatives we calculated above together, so our final answer is:
This can be simplified in several ways, but one simplified version of the derivative may be:
Another method, using the chain rule along with the trigonometric identity