Simplify a Differential please

[nil101]

Hi
Can you help me simplify the following differential?

\(\displaystyle \L \b
y = x^2 (\sqrt x - 2)\)

\(\displaystyle \L u = x^2 {\rm }u' = 2x\)

\(\displaystyle \L v = (x)^{{\textstyle{1 \over 2}}} - 2{\rm }v' = \frac{1}{2}(x)^{ - {\textstyle{1 \over 2}}}\)

\(\displaystyle \L
\frac{{dy}}{{dx}} = 2x(x^{{\textstyle{1 \over 2}}} - 2) + \frac{1}{2}x^2 (x)^{ - {\textstyle{1 \over 2}}}\)

\(\displaystyle \L
= 2x(\sqrt x - 2) + \frac{{x^2 }}{{2\sqrt x }}\)

I try to simplify by multiplying through by \(\displaystyle \b {2\sqrt x }\) but it quickly gets messy.

Can you help?

Thanks

 

[pka]

Just note that \(\displaystyle \L
x^2 \left( {\sqrt x - 2} \right) = x^{\frac{5}{2}} - 2x^2\)

 

[nil101]

Thanks pka. That makes it much easier.