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!!

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- Jan 19th 2009, 10:13 AMjanedoeDerivative 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!! - Jan 19th 2009, 10:37 AMgalactus
They did this:

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

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

Note: I used h instead of $\displaystyle {\Delta}x$. Same thing - Jan 19th 2009, 10:43 AMjanedoe
I got that too but I don't understand what comes next..can you please show me the next steps?

- Jan 19th 2009, 11:02 AMJester
- Jan 19th 2009, 11:25 AMjanedoe
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?

- Jan 19th 2009, 12:31 PMJester
$\displaystyle

\lim_{h\to 0}\frac{\sqrt{x}-\sqrt{x+h}}{h\sqrt{x+h}\sqrt{x}}$$\displaystyle = \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 $\displaystyle h$ in the bottom, then take the limit. :)