# Math Help - Derivative problem...how did they get this answer?

1. ## Derivative problem...how did they get this answer?

http://i43.tinypic.com/2j11mgy.jpg --> problem is here

I only would like to know how they got that from the derivative equation. Can you please show me step by step how you'd go about doing it, using that formula?

Thanks!!

2. They did this:

$\lim_{h\to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt{x}}}{h}$

How, work the algebra magic, take the limit as h approaches 0 and you have it. The derivative of $\frac{1}{\sqrt{x}}$

Note: I used h instead of ${\Delta}x$. Same thing

3. I got that too but I don't understand what comes next..can you please show me the next steps?

4. Originally Posted by galactus
They did this:

$\lim_{h\to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt{x}}}{h}$

How, work the algebra magic, take the limit as h approaches 0 and you have it. The derivative of $\frac{1}{\sqrt{x}}$

Note: I used h instead of ${\Delta}x$. Same thing
Next hint, simplify what Galactus has as

$\lim_{h\to 0}\frac{\sqrt{x}-\sqrt{x+h}}{h\sqrt{x+h}\sqrt{x}}$ then rationalize.

5. I did that and got your answer but now I'm having trouble rationalizing...could you show me how to go about that with this problem?

6. Originally Posted by janedoe
I did that and got your answer but now I'm having trouble rationalizing...could you show me how to go about that with this problem?
$
\lim_{h\to 0}\frac{\sqrt{x}-\sqrt{x+h}}{h\sqrt{x+h}\sqrt{x}}$
$= \lim_{h\to 0}\frac{\sqrt{x}-\sqrt{x+h}} {h\sqrt{x+h}\sqrt{x}}\cdot \frac{\sqrt{x}+\sqrt{x+h}}{\sqrt{x}+\sqrt{x+h}}$

Expand only the numerator and things in the top will cancel, then cancel the $h$ in the bottom, then take the limit.