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

2 Answers
Mar 30, 2018

Answer:

#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

Answer:

#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#