Question

How do you use the Product Rule to find the derivative of `y = x^2 (x^2 + 1)^5`?

Answer 1

`dy/dx=2x(x^2+1)^4(6x^2+1)`

Explanation:

The product rule states:
`f=gh=>f'=g'h+gh'`

For this function we have:
`f(x)=y, g(x)=x^2, h(x)=(x^2+1)^5`
`g'(x)=2x, h'(x)=10x(x^2+1)^4`

Therefore by the charnel we have:
`dy/dx=g'h+gh'=2x(x^2+1)^5+10x^3(x^2+1)^4=2x(x^2+1)^4(6x^2+1)`