Question

What is the correct way to solve this? Explain in steps. Thank you.

Answer 1

Use chain rule

Explanation:

`f(x) = u/v`
`f'(x) = (vdu-udv)/v^2`

Use this relationship to compute the derivative

`u = (1+sqrt(3x))` and `v = (1-sqrt(3x))`
`du = sqrt(3)/(2sqrt(x))`
`dv = -sqrt(3)/(2sqrt(x))`

`f'(x)=(((1-sqrt(3x))sqrt(3))/(2sqrt(x))+((1+sqrt(3x))sqrt(3))/(2sqrt(x)))/(1-sqrt(3x))^2`

-`f'(x) =(sqrt(3)(1-\cancel(sqrt(3x))+1+\cancel(sqrt(3x))))/(2sqrt(x)(1-sqrt(3x))^2`

`f'(x) =3/(sqrt(3x)(1-sqrt(3x))^2`