[SOLVED] Derivative Problem

**Ian1779** · August 1st 2009, 02:48 PM

Hi

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

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

where

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

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

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

Thanks

**Plato** · August 1st 2009, 03:00 PM

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

In general $<br /> \frac{{d\sqrt f }}<br /> {{dx}} = \frac{{f'}}<br /> {{2\sqrt f }}$

**Ian1779** · August 1st 2009, 03:08 PM

Thanks so much - it makes sense now!!

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