Question

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

Answer 1

`g'(x)=2x(x^2+1)^5+10x(x^2+1)^4(x^2-1)`

Explanation:

I presume the question contains a typographical error and it was meant `g(x)` and not `g(y)` for if `g(y)` was intended, then the derivative is simply `g'(y)=0`.

Suppose `g(x)=(x^2+1)^5(x^2-1)`.

Then the derivative may be found by using the product rule together with the power rule as follows

`g'(x)=2x(x^2+1)^5+5(x^2+1)^4(2x)(x^2-1)`