Question

find the derivative of y with respect to x.

y=tan^-1 (sqrt 3x)

Answer 1

use the chain rule.
you have 3 functions that are composed
\[ f(x)=\arctan x=tan^{-1}x \]
\[ g(x)=\sqrt{x} \]
\[ h(x)=3x \]
so
\[ y=(f\circ g\circ h)(x) \]
and the chain rule gives you
\[\LARGE y'=(f'\circ g\circ h)(x)\cdot(g'\circ h)(x)\cdot h'(x) \]
try it!

Answer 2

or you can draw a triangle...