# How do you differentiate #g(y) =(x^2 - 2x + 1)^4 (4x^6 + 5) # using the product rule?

##### 1 Answer

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#### Explanation

#### Explanation:

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Treat the two terms as a normal product rule, but then use the chain rule on the first function when differentiating to get the full solution:

#### Explanation:

First, let's designate the two pieces of the function as

For a given function, the derivative using the product rule is:

This means we'll need to know the derivatives of each

Deriving

Deriving

Now, we reassemble (and simplify):

Note that the factored form of

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