Originally Posted by

**Maskawisewin** I'm having an issue with the following derivative.

$\displaystyle y=\frac{x^3-3x^2+2\sqrt{x}-5}{\sqrt{x}}$

I use the product rule and get up to this point:

$\displaystyle =\frac{3x^2-6x+x^{-1/2}}{\sqrt{x}}-\frac{x^3-3x^2+2x^{1/2}-5}{2\sqrt{x^3}}$

Wolfram Alpha tells me the answer is:

$\displaystyle =\frac{5x^3-9x^2+5}{2\sqrt{x^3}}$

My fraction skills are not the best-- far from best. I tried multiplying the left side by $\displaystyle \frac{2\sqrt{x}}{2\sqrt{x}}$ but that made a big mess. Maybe it was the right thing to do but I just made a mess and couldn't see how to make it work. Thanks for any help. I've recently returned to school after a 17 year hiatus.