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 $\frac{2\sqrt{x}}{2\sqrt{x}}$.

3. Re: Simplifying derivatives

Doesn't that just move the $\sqrt{x}$ to the denominator?

I would combine the terms in the numerator and multiply by $\frac{2}{2}$ to get the $\frac{1}{2}$ out of the numerator.

- Hollywood

4. Re: Simplifying derivatives

Originally Posted by hollywood
Doesn't that just move the $\sqrt{x}$ 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 $x^{\frac{1}{2}}$ where it clearly said $x^{-\frac{1}{2}}$.

The correct original expression is:

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

which can be multiplied by $\frac{2\sqrt{x}}{2\sqrt{x}}$ (as you said) to get

$\frac{1-5x^3}{2\sqrt{x}(x^3+1)^2}$.

Thanks,
Hollywood