## Using the definintion, find the derivative of f(x) = 1/x.

Limits, differentiation, related rates, integration, trig integrals, etc.
nona.m.nona
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### Using the definintion, find the derivative of f(x) = 1/x.

Using the definintion, find the derivative of f(x) = 1/x.

The definition is $f'(x)=\lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h}$

First I did the numerator:

$\frac{1}{x+h}-\frac{1}{x}$

$\frac{x}{x(x+h)}-\frac{x+h}{x(x+h)}$

$\frac{-h}{x(x+h)}$

Then I put the denominator in:

$\frac{\left(\frac{-h}{x(x+h)}\right)}{h}$

$\frac{-h}{xh(x+h)}=\frac{-1}{x(x+h)}$

Then the limit gives me $-\frac{1}{x^2}$

Did I do this correctly? Thank you.

Martingale
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Joined: Mon Mar 30, 2009 1:30 pm
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yes