# What is the derivative of #sin^2(x) * cos^2(x)#?

##### 2 Answers

By the chain and product rules,

#### Explanation:

In order to evaluate this derivative, we need to use both the product and chain rules.

Starting with

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:

#### Explanation:

Another method, using the chain rule along with the trigonometric identity

#=1/4d/dxsin^2(2x)#

#=1/4*2sin(2x)(d/dxsin(2x))#

#=sin(2x)/2*cos(2x)(d/dx2x)#

#=(sin(2x)cos(2x))/2*2#

#=sin(2x)cos(2x)#