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