# How do you use the Product Rule to find the derivative of #sin(3x) cos(5x) #?

##### 1 Answer

#### Answer:

#### Explanation:

First, notice that you can write your function as a product of two functions,

#y = f(x) * g(x)#

The product rule allows you to differentiate such functions by using the formula

#color(blue)(d/dx(y) = [d/dx(f(x))] * g(x) + f(x) * d/dx(g(x)))#

In your case, you have

Now, in order to differentiate these two functions, you need to use the chain rule in the form

This will get you

and

Your target derivative will thus be