Trying to find the derivative and I am stuck on simplifying it.
What do I do after this step?
Doesn't that just move the $\displaystyle \sqrt{x}$ to the denominator?
I would combine the terms in the numerator and multiply by $\displaystyle \frac{2}{2}$ to get the $\displaystyle \frac{1}{2}$ out of the numerator.
- Hollywood
Oops - I was reading $\displaystyle x^{\frac{1}{2}}$ where it clearly said $\displaystyle x^{-\frac{1}{2}}$.
The correct original expression is:
$\displaystyle \frac{(x^3+1)(\frac{1}{2}x^{-\frac{1}{2}})-(x^{\frac{1}{2}})(3x^2)}{(x^3+1)^2}$
which can be multiplied by $\displaystyle \frac{2\sqrt{x}}{2\sqrt{x}}$ (as you said) to get
$\displaystyle \frac{1-5x^3}{2\sqrt{x}(x^3+1)^2}$.
(unless I've made another mistake.....)
Thanks,
Hollywood