# How do you differentiate #f(x)= (3x+1)^4(2x-3)^3 # using the product rule?

##### 1 Answer

#### Answer:

#### Explanation:

This problem actually involves two rules: the product rule, and the chain rule. But first, let's just focus on the product rule. The general equation for this is:

Now, we just plug in everything:

The problem arises at the fact that your two functions are actually compositions of functions. For example,

So first, we do the outermost function (in this case

=>

=>

=>

Now, for the second one:

Again, same process. Derivative of the outside, then multiply by derivative of the inside:

=>

=>

=>

We're done! Now, we just go ahead and plug these back into the product rule equation we got for our final answer:

You could foil out some stuff here, but in my opinion, it's really just more work. Easier to leave it as is.

Hope that helped :)