Question

Derivative question

Answer 1

Find f'(a).
f(x) = x^-2

Answer 2

Here is what I have so far:
(x+h)^-2 - (x)^-2 all over h
.....what now?

Answer 3

If you could do the other one, do this the same way.

Answer 4

Write them as fractions, common denoms, do math.

Answer 5

I got it down to:
\[\frac{ 2x+h }{ x^2(x+h)^2 }\]

Answer 6

What should I do next?

Answer 7

Plug in h=0!

Answer 8

But i feel like you've made a minor mistake, the deriv. should be negative.

Answer 9

\[\frac{ 2 }{ x^3 }\]
But negative?

Answer 10

yes, it should be negative.
\[ \lim_{h\rightarrow 0}\frac{1}{h}\left( \frac{1}{(x+h)^2}- \frac{1}{x^2} \right) \]

Answer 11

\[ \lim_{h\rightarrow 0}\frac{1}{h} \left(\frac{x^2-(x+h)^2}{x^2(x+h)^2} \right) \]

Answer 12

is that what you did ?