# Derivative help needed

• Feb 11th 2008, 04:14 PM
CenturionMonkey
Derivative help needed
Hey guys I need help with this problem. I have to find the derivative using the formula:
$\displaystyle \lim_{h \to 0} \frac {f(x + h) - f(x)}h$

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

• Feb 11th 2008, 06:42 PM
Jhevon
Quote:

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

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

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

so what is $\displaystyle f(x + h)$ here?
• Feb 11th 2008, 06:55 PM
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 $\displaystyle f(x)=\sqrt{x}-x$
• Feb 11th 2008, 07:09 PM
Jhevon
Quote:

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 $\displaystyle f(x)=\sqrt{x}-x$

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

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

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

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