Question

How do you differentiate `f(x)=(ln(6x+8))^2` using the chain rule.?

Answer 1

I found: `f'(x)=6/(3x+4)ln(6x+8)`

Explanation:

First derive the `()^2` as it is then multiply by the derivative of the `ln` (red) and finally multply by the derivative of the argument of the `ln` (blue):
`f'(x)=2(ln(6x+8))^(2-1)*color(red)(1/(6x+8))*color(blue)(6)=`
`=12/(6x+8)ln(6x+8)=12/(2(3x+4))ln(6x+8)=`
`=6/(3x+4)ln(6x+8)`