# Math Help - derivative of arctan2x^1/2

1. ## derivative of arctan2x^1/2

[QUOTE=Quacky;694202]Let's see.

$y = \sqrt{arctan2x}$
$y^2 = arctan2x$
$tany^2 = 2x$
$\frac {dy}{dx} * sec^2y^2$ $tany^2 = 2$

How do I differentiate from here? I get $\frac {dy}{dx} = \frac {1}{4x^3+x}$ as an answer

2. ## Re: derivative of arctan2x^1/2

[QUOTE=Barthayn;696842]
Originally Posted by Quacky
Let's see.

$y = \sqrt{arctan2x}$
$y^2 = arctan2x$
$tany^2 = 2x$
$\frac {dy}{dx} * sec^2y^2$ $tany^2 = 2$

How do I differentiate from here? I am lost because of the $y^2$
Use implicit differentiation and the chain rule.

The derivative of $\tan(y^2)$ is $2y \sec^2(y^2) \cdot \dfrac{dy}{dx}$

3. ## Re: derivative of arctan2x^1/2

let $u = 2x$

$y = \left(\arctan{u}\right)^{1/2}$

$y' = \frac{1}{2}\left(\arctan{u}\right)^{-1/2} \cdot \frac{u'}{1+u^2}$

4. ## Re: derivative of arctan2x^1/2

thanks, I got it now