# How do you differentiate #f(x)=(1/x^3)sinx# using the product rule?

##### 1 Answer

May 25, 2018

#### Explanation:

Let's start by rewriting

We understand that if we have two functions,

#color(blue)(g(x)=x^-3)# #color(red)(h(x)=sinx)#

We can use the power rule and our knowledge of trig derivatives to figure out that

#color(purple)(g'(x)=-3x^-4)# #color(lime)(h'(x)=cosx)#

Now, we just plug this business into our expression for the product rule. We get

And I can write this with neutral colors to get

Hope this helps!