Question

How do you find the derivative of `q(x) = (8x) ^(2/3)` using the chain rule?

Answer 1

I found: `q'(x)=8/(3root3(x))`

Explanation:

First derive as a normal exponent (in red) and then multiply by the derivative of the argument (in blue):
`q'(x)=color(red)(2/3(8x)^(2/3-1))*color(blue)(8)=`
`=16/3(8x)^(-1/3)=`
`=16/3*1/root3(8x)=`
`=16/3*1/(2root3(x))=8/(3root3(x))`