Question

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

Answer 1

`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}`