Derivative

**wowo** · October 17th 2010, 02:47 PM

Hi.
How to find the derivative of 1/(x^2) using definition of the derivative;I know how to find it by using the power rule but not the definition

.

Thanks.

**lvleph** · October 17th 2010, 02:51 PM

The definition of the derivative is: If $f(x) = \frac{1}{x^2}$ then
$f'(x) = \lim_{h\to 0} \frac{f(x+h) - f(x)}{h}$
So try doing that and come back and tell us how you did. We can help you if you still need help.

**wowo** · October 17th 2010, 03:06 PM

I need a hint, 'cause I'm still stuck.

**lvleph** · October 17th 2010, 03:07 PM

Tell me what f(x+h) and f(x) are, then tell post what $\frac{f(x+h) - f(x)}{h}$ . Once you have all that you should be able to simplify things and take the derivative.

**skeeter** · October 17th 2010, 03:09 PM

$\displaystyle f'(x) = \lim_{h \to 0} \frac{\frac{1}{(x+h)^2} - \frac{1}{x^2}}{h}$

start by getting a common denominator and get those two fractions in the numerator together.

**wowo** · October 17th 2010, 03:35 PM

I keep getting lost during simplifying process.

(what's wrong with me

)

**skeeter** · October 17th 2010, 03:43 PM

Originally Posted by wowo

I keep getting lost during simplifying process. what's wrong with me

can' say ... you haven't shown anything other than posting the problem.

start by getting these two fractions together ...

$\displaystyle \frac{1}{(x+h)^2} - \frac{1}{x^2}$

... note that the common denominator is $x^2(x+h)^2$ .

do it.

**wowo** · October 17th 2010, 03:53 PM

$x^2-1(x^2+2xh+h^2)/(x^2+2xh+h^2)(x^2)/h$

Am I right????

**lvleph** · October 17th 2010, 03:55 PM

Yes, continue simplification. Eventually an h will cancel.

**skeeter** · October 17th 2010, 03:55 PM

Originally Posted by wowo

$x^2-1(x^2+2xh+h^2)/(x^2+2xh+h^2)(x^2)/h$

Am I right????

keep going ... clean it up

**wowo** · October 17th 2010, 04:26 PM

Okay, I'm completely lost with simplifying

**skeeter** · October 17th 2010, 04:32 PM

Originally Posted by wowo

Okay, I'm completely lost with simplifying

$\displaystyle \frac{1}{h} \left[\frac{x^2 - (x^2 + 2xh + h^2)}{x^2(x+h)^2}\right]$

distribute the negative in the numerator and combine like terms ... then factor out an $h$ from what's left in the numerator ...

**wowo** · October 17th 2010, 04:58 PM

So, It's $2x+h/(x^2(x+h)^2$
$2x/(x^2)(x^2)$
$2/x^3$

**mr fantastic** · October 17th 2010, 05:09 PM

Originally Posted by wowo

So, It's $2x+h/(x^2(x+h)^2$
$2x/(x^2)(x^2)$
$2/x^3$

No. You have made a careless mistake in the numerator. Go back, check your work, find the mistake. Hint: You know what the final answer is meant to be, don't you ....?

**wowo** · October 17th 2010, 05:22 PM

Is it -2x+h/(x^2(x+h)^2 ??

Thread: Derivative

LinkBack

Thread Tools

Display

Derivative

Similar Math Help Forum Discussions

contuous weak derivative $\Rightarrow$ classic derivative ?

Expanding a time derivative in terms of other variables /// Material derivative

[SOLVED] Definition of Derivative/Alt. form of the derivative

derivative of 1/[sqrt[x]: proving with derivative definition

Derivative of definate intagral / second derivative? idk.

Search Tags