How do you find the derivative of f(x) = (x^2+1)^3?

2 Answers
Mar 30, 2018

6x*(x^2+1)^2

Explanation:

You use the chain rule and bring down the 3 and find the derivative of x^2+1. The derivative is 2x. So, the answer is 2x*3*(x^2+1)^2. The final answer is 6x*(x^2+1)^2

Mar 30, 2018

6x(x^2+1)^2

Explanation:

We use the chain rule, which states that,

dy/dx=dy/(du)*(du)/dx

Let u=x^2+1,:.(du)/dx=2x.

We also have y=u^3,:.dy/(du)=3u^2.

Multiplying together, we get,

dy/dx=3u^2*2x

=6xu^2

Undoing the substitution that u=x^2+1, we get:

=6x(x^2+1)^2