First Principles... 1/x^2 really can't do this...

• May 11th 2011, 09:54 AM
Snaggle
First Principles... 1/x^2 really can't do this...
Differentiate 1/x^2 from first principles..
Would love someone to help me with this!
• May 11th 2011, 09:55 AM
Ackbeet
What do you mean by "first principles"? Do you mean the limit definition of the derivative? Or from using basic derivative theorems? Or what?
• May 11th 2011, 09:56 AM
TheEmptySet
Quote:

Originally Posted by Snaggle
Differentiate 1/x^2 from first principles..
Would love someone to help me with this!

What have you tried?

The defintion is

$f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}$
• May 12th 2011, 06:30 AM
HallsofIvy
$\frac{\frac{1}{(x+ h)^2}- \frac{1}{x^2}}{h}= \frac{\frac{x^2}{x^2(x+h)^2}- \frac{(x+h)^2}{x^2(x+h)^2}}{h}$
$= \frac{x^2- (x+h)^2}{hx^2(x+ h)^2}$

You should be able to now reduce that to something that has a limit as x goes to 0.

Okay, the first post I did this morning, I used "tex" and it didn't work so I went back to "math" and that did work. "Great" I thought- they have that fixed now. But on this post I used "math" and it didn't work- I had to use "tex". What is going on?