Question

Find the derivative of..

Answer 1

\[\LARGE y = 11 arctan~(\sqrt{x}) \]

Answer 2

do you know the derivative of arctan(x) ?

Answer 3

Uhm..
\[\LARGE \frac{1}{1+x^2}\]?

Answer 4

yes

Answer 5

if we use "u" instead of x
\[ \frac{d}{du}\arctan(u) = \frac{1}{1+u^2} \]
if we want the derivative with respect to x, and u is a function of x, we use the chain rule
\[ \frac{d}{dx}\arctan(u) = \frac{1}{1+u^2} \frac{du}{dx}\]

Answer 6

in your case, let
\[ u = \sqrt{x} = x^{\frac{1}{2}} \]

Answer 7

as for the 11, factor that out. It will multiply the final answer.

Answer 8

That actually makes it easier, thanks :)