(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the derivative using the Definition of the Derivative:

f(x) = 1 / x^2

2. Relevant equations

The Definition:

f`(a) = lim h->0 [f(a+h) - f(a)] / h

3. The attempt at a solution

This is what I did:

f`(a) = lim h->0 [tex](1/(x+h)^{2}) - 1/x^{2}) / (h)[/tex]

f`(a) = lim h->0 [tex][((x^{2}) - 1 (x^{2} + 2xh + h^{2})) / x^{2}(x^{2} + 2xh + h^{2})] / h[/tex]

f`(a) = lim h->0 [tex](2x + h) / (x^{4} + 2x^{3}h + x^{2}h^{2})[/tex]

and finally

f`(a) = lim h->0 [tex]2 / x^{3}[/tex]

So I got that as the derivative, and if I did it correctly it should be right. Did I use the definition properly?

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# Homework Help: Definition of Derivative

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