Question

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

Answer 1

`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`

Answer 2

`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`