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

Dec 26, 2015

$g ' \left(x\right) = 2 x {\left({x}^{2} + 1\right)}^{5} + 10 x {\left({x}^{2} + 1\right)}^{4} \left({x}^{2} - 1\right)$

#### Explanation:

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

Suppose $g \left(x\right) = {\left({x}^{2} + 1\right)}^{5} \left({x}^{2} - 1\right)$.

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

$g ' \left(x\right) = 2 x {\left({x}^{2} + 1\right)}^{5} + 5 {\left({x}^{2} + 1\right)}^{4} \left(2 x\right) \left({x}^{2} - 1\right)$