How do you differentiate #f(x)=(x^2+1)^3# using the chain rule?

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Answer 1 · 2015-11-06T15:46:03

#f'(x)=6x(x^2+1)^2#

Let #u=x^2+1#.

#frac{du}{dx}=2x#

#f(x)=u^3#

#f'(x)=frac{d(u^3)}{dx}#

#=frac{d(u^3)}{du}frac{du}{dx}#

#=(3u^2)(2x)#

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