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How do you use the chain rule to differentiate #root3(-4x)#?

1 Answer

Nov 22, 2016

#f'(x)=frac{-4}{3(-4x)^(2/3)}#

Explanation:

#root3(-4x)#
Let #f(x)=(-4x)^(1/3)#

Use the chain rule to differentiate. In simplest terms, the chain rule is to "take the derivative of the outside times the derivative of the inside".

#f'(x)=(1/3)(-4x)^(-2/3)(-4)#
#f'(x)=frac{-4}{3(-4x)^(2/3)}#
#f'(x)=frac{-4}{3root3(-4x)^2}#

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