differentiation

[Lippi86]

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Consider the function f(x)=-1/x. Find the derivative of this function using the definition of the derivative....

I know that the definition looks like f´(x)=lim h-->0 f(x+h)-f(x)/h

But then?

Thanks for any kind of answers=)

 

[galactus]

\(\displaystyle f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}\)

The algebra is what kills most with these problems.

\(\displaystyle =\lim_{h\to 0}\frac{\frac{-1}{x+h}+\frac{1}{x}}{h}\)

\(\displaystyle =\lim_{h\to 0}\frac{1}{x(x+h)}\)

Now, see it?.