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

1. ## 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!

2. What do you mean by "first principles"? Do you mean the limit definition of the derivative? Or from using basic derivative theorems? Or what?

3. 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

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

4. $\displaystyle \frac{\frac{1}{(x+ h)^2}- \frac{1}{x^2}}{h}= \frac{\frac{x^2}{x^2(x+h)^2}- \frac{(x+h)^2}{x^2(x+h)^2}}{h}$
$\displaystyle = \frac{x^2- (x+h)^2}{hx^2(x+ h)^2}$

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?

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# find the derivative of 1/x^2 using first principles

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