## anonymous 5 years ago Using definition of derivative prove that (1/x)'=-1/x^2

1. anonymous

Example 2: (d/dx)(1/x) = -1/(x2) f(x) = 1/x f'(x) = (d/dx)(1/x) = (d/dx)(x-1) = (-1)x-2 = -1/(x2)

2. amistre64

(1/x)' = -1/x^2 D(1/x) = -1/x^2 x(0) - 1(1) --------- = -1/x^2 x^2 -1/x^2 = -1/x^2

3. nikvist

$f'(x)=\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h} =\lim_{h\rightarrow 0}\frac{\frac{1}{x+h}-\frac{1}{x}}{h}= \lim_{h\rightarrow 0}\frac{-1}{x(x+h)}=-\frac{1}{x^2}$

4. amistre64

hmmm.... i spose that would be more accutate depending on your definition of a derivative :)