I'm not too sure if I'm approaching the question correctly:

(a)Find$\displaystyle \frac {d}{dx} [\frac {-1}{\sqrt{1+x^2}}]$(b)Hence evaluate$\displaystyle \\ \int_0^2 {\frac{x}{(1+x^2)^\frac{3}{2}}}dx$

And this is my attempt:

(a)Find$\displaystyle \frac {d}{dx} [\frac {-1}{\sqrt{1+x^2}}]$

$\displaystyle = \frac{2x}{2(x^2 +1)^\frac{3}{2}}$

(b)Hence evaluate$\displaystyle \int_0^2 {\frac{x}{(1+x^2)^\frac{3}{2}}}dx$

$\displaystyle =-\frac {1}{\sqrt{x^2 +1}}\\\\for 2\\=-\frac {1}{\sqrt{5}}\\\\for 0\\\\=-1\\\\=-\frac {1}{\sqrt{5}}-(-1)\\\\= 1-\frac {1}{\sqrt{5}} \approx 0.553$

Help much appreciated!