Question

(i know i've asked so many questions. i just want to make sure my answers are right for this homework! hopefully it isn't too annoying for you :) )

Find the derivative of the given function. y=(tan^-1)√(3x)
A. (1)/(√(1-3x))
B. (1)/(6√(3x(1+3x)))
C. (3)/(2(1+3x)√(3x))
D. (1)/(1+3x)

My answer was D. Although when I computed the answer and did tan^-1 as arctan, I kept getting (1)/(3x^2 +1) as my answer but it wasn't a choice. Am I doing something wrong? Again, so so sorry for asking so many questions.

Answer 1

since (arctan(u))' = 1/(1+u^2) u', we have

d/dx arctan √(3x)
= 1/(1+3x) (√3)/(2√(3x))
= √3 / (6x+2)√x

Answer 2

So, looks like C to me.