1. ## [SOLVED] Derivative Problem

Hi

I am trying to differentiate the following using the Product rule,

$\displaystyle \frac{d}{dx}arcsin (2x)\sqrt{1-4x^2}$

where

$\displaystyle f(x) = arcsin (2x)$
$\displaystyle g(x) =\sqrt{1-4x^2}$

$\displaystyle f'(x)g(x)$ simplifes to 2 but I am stuck on $\displaystyle f(x)g'(x)$

I have changed $\displaystyle \sqrt{1-4x^2}$ to $\displaystyle (1-4x^2)^\frac{1}{2}$ before differentiating but not clear what to do next.

Thanks

2. $\displaystyle \frac{{d\sqrt {1 - 4x^2 } }}{{dx}} = \frac{{ - 8x}}{{2\sqrt {1 - 4x^2 } }}$

In general $\displaystyle \frac{{d\sqrt f }} {{dx}} = \frac{{f'}} {{2\sqrt f }}$

3. Thanks so much - it makes sense now!!