# Thread: differentiating a function from first principles

1. ## 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?

2. ## Re: differentiating a function from first principles

I have found I have done this question before. It involves making a common denominator.

3. ## Re: differentiating a function from first principles

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...

4. ## 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 ...