# How do you use the Product Rule to find the derivative of #f(z) = z^3sin^2(2z)#?

##### 1 Answer

Oct 19, 2015

#### Answer:

See the explanation.

#### Explanation:

I assume that he challenge is to differentiate

Note that

So the derivative is

# = 2[sin(2z)] (cos(2z) (2)#

# = 4sin(2z)cos(2z)#

This last expression can be rewritten as

Now to the big question:

# = 3z^2sin^2(2z) + 4z^3sin(2z)cos(2z)#

Rewrite/simplify to taste.