Question

derivative y=tan^-1√3x

Answer 1

\[\frac{d}{dx}\tan^{-1}(\sqrt{3x})\] like that?

Answer 2

i mean is the radical over all of the inside piece? \(\sqrt{3x}\)??

Answer 3

yes

Answer 4

ok then we need two facts:
one fact is \(\frac{d}{dx}\tan^{-1}(x)=\frac{1}{x^2+1}\)
the other is \(\frac{d}{dx}\sqrt{x}=\frac{1}{2\sqrt{x}}\) and also chain rule

Answer 5

this gives
\[\frac{d}{dx}\tan^{-1}(\sqrt{3x})=\frac{1}{(\sqrt{3x})^2+1}\times \frac{\sqrt{3}}{2\sqrt{x}}\] which you can clean up via some algebra

Answer 6

if there is a part there that is not clear, let me know

Answer 7

thank you!

Answer 8

yw