# Thread: Simplifying derivatives

1. ## Simplifying derivatives

Trying to find the derivative and I am stuck on simplifying it.

What do I do after this step?

2. ## Re: Simplifying derivatives

Originally Posted by minneola24
Trying to find the derivative and I am stuck on simplifying it.

What do I do after this step?
Multiply by $\displaystyle \frac{2\sqrt{x}}{2\sqrt{x}}$.

3. ## Re: Simplifying derivatives

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

4. ## Re: Simplifying derivatives

Originally Posted by hollywood
Doesn't that just move the $\displaystyle \sqrt{x}$ to the denominator?

What wrong with that?
In fact, I is the form I required from students.

5. ## Re: Simplifying derivatives

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