Derivative help needed

**CenturionMonkey** · February 11th 2008, 04:14 PM

Hey guys I need help with this problem. I have to find the derivative using the formula:
$\lim_{h \to 0} \frac {f(x + h) - f(x)}h$

and the question is $f(x) = \sqrt{x} - x$

please and thank you.

**Jhevon** · February 11th 2008, 06:42 PM

Originally Posted by CenturionMonkey

Hey guys I need help with this problem. I have to find the derivative using the formula:
$(f(x+h) - f(x))/h$

and the question is $f(x) = \sqrt{x} - x$

please and thank you.

you mean you want $\lim_{h \to 0} \frac {f(x + h) - f(x)}h$

so what is $f(x + h)$ here?

**CenturionMonkey** · February 11th 2008, 06:55 PM

yes that's what I mean (I edited my post, I didn't know how to do the fancy math for that.) But I need the derivative of $f(x)=\sqrt{x}-x$

**Jhevon** · February 11th 2008, 07:09 PM

Originally Posted by CenturionMonkey

yes that's what I mean (I edited my post, I didn't know how to do the fancy math for that.) But I need the derivative of $f(x)=\sqrt{x}-x$

yes, i know. that's why i asked you what f(x + h) was, you need to plug it in...

you want $f'(x) = \lim_{h \to 0} \frac {\sqrt{x + h} - x - h - \sqrt{x} + x}h$

$\Rightarrow f'(x) = \lim_{h \to 0} \frac {\sqrt{x + h} - h - \sqrt{x}}h$

now multiply by $\frac {\sqrt{x + h} + h + \sqrt{x}}{\sqrt{x + h} + h + \sqrt{x}}$ and continue

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