# differentiating a function from first principles

• Sep 17th 2011, 09:02 AM
Stuck Man
differentiating a function from first principles
lim &#40;&#40;x&#43;h&#41;&#94;-2 - x&#94;-2&#41;&#47;h as h->0 - Wolfram|Alpha

I don't know where the answer is coming from. What are the missing steps?
• Sep 17th 2011, 09:06 AM
Stuck Man
Re: differentiating a function from first principles
I have found I have done this question before. It involves making a common denominator.
• Sep 17th 2011, 09:06 AM
Prove It
Re: differentiating a function from first principles
Quote:

Originally Posted by Stuck Man
lim &#40;&#40;x&#43;h&#41;&#94;-2 - x&#94;-2&#41;&#47;h as h->0 - Wolfram|Alpha

I don't know where the answer is coming from. What are the missing steps?

Try getting a common denominator, then expanding the numerator...
• Sep 17th 2011, 11:17 AM
skeeter
Re: differentiating a function from first principles
$\lim_{h \to 0} \frac{\frac{1}{(x+h)^2} - \frac{1}{x^2}}{h}$

$\lim_{h \to 0} \frac{\frac{1}{(x+h)^2} - \frac{1}{x^2}}{h} \cdot \frac{x^2(x+h)^2}{x^2(x+h)^2}$

$\lim_{h \to 0} \frac{x^2 - (x+h)^2}{h \cdot x^2(x+h)^2}$

finish it ...