# Math Help - Beginner in finding derivative of a function...

1. ## Beginner in finding derivative of a function...

Find the derivative of:

$f(x) = \sqrt {(x^2 + 1)(\sqrt x + 1)^3 }$

My work so far:

$f'(x) = \frac{1}
{2}[(x^2 + 1)(\sqrt x + 1)^3 ]^{ - \frac{1}
{2}} \bullet \frac{d}
{{dx}}[(x^2 + 1)(\sqrt x + 1)^3$

$
f'(x) = \frac{1}
{2}[(x^2 + 1)(\sqrt x + 1)^3 ]^{ - \frac{1}
{2}} \bullet (2x)(\sqrt x + 1)^3 + (x^2 + 1)3(x^{\frac{1}
{2}} + 1)^2$

2. ## Close

You're close, but just a little off on your last shown step:
$\frac{d}{dx}(\sqrt{x}+1)^3=3(\sqrt{x}+1)^2\cdot\fr ac{d}{dx}\sqrt{x}$, via the chain rule, so the last line should be:
$f'(x)=\frac{1}{2}[(x^2+1)(\sqrt{x}+1)^3]^{-\frac{1}{2}}\cdot\left[(2x)(\sqrt{x}+1)^3+(x^2+1)\cdot3(\sqrt{x}+1)^2\fra c{1}{2}x^{-\frac{1}{2}}\right]$
Which can be simplified via algebra.

--Kevin C.