# Find the derivative using the definition only!

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• March 25th 2010, 04:18 PM
frenchguy87
Find the derivative using the definition only!
How would you show that the derivative of $f(x) = \frac{1}{\sqrt{x}}$ is equal to $\frac{1}{2\sqrt{x^3}}$ for $x>0$ , using the definition of a derivative??

I started and got lost in the calculation...

I have to start with the following
$| \frac{\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{c}}}{x-c} + \frac{1}{2\sqrt{c^3}} |$ and show I can make it less than $\epsilon$ , which is just the definition

I know I have $|x-c|<\delta$ to play with... can anyone help me out? this is due tomorrow so the more you can give me the better lol thanks
• March 25th 2010, 04:33 PM
Random Variable
If you're looking to find the derivative from the definition, check out this thread: http://www.mathhelpforum.com/math-he...ve-answer.html

But it looks like you're trying to prove the existence of a limit.
• March 25th 2010, 04:36 PM
frenchguy87
thanks that works