# Math Help - 2nd derivative help

1. ## 2nd derivative help

Hi,

Could someone point me in the right direction please.

I need to know how to find the second derivative of arccos x, I know the first derivative is -1/sqroute 1 - x^2, but don't know what to do now to get the second derivative?

Any help much appreciated,

2. Originally Posted by joemc22
Hi,

Could someone point me in the right direction please.

I need to know how to find the second derivative of arccos x, I know the first derivative is -1/sqroute 1 - x^2, but don't know what to do now to get the second derivative?

Any help much appreciated,
$-\frac{1}{\sqrt{1-x^2}} = -(1-x^2)^{-\frac{1}{2}}$

using the chain rule ...

$\frac{1}{2}(1-x^2)^{-\frac{3}{2}} \cdot (-2x)$

clean up the algebra ...

$-\frac{x}{(1-x^2)^{\frac{3}{2}}}
$