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If f is a continuous function on the interval (a,b), then the f', the derivative of f, is defined as the limit,

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

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d Sin proves that the derivative of the sine function is the cosine.
L'Hopital's Rule gives you a way to find the limit as x−>c of f(x)/g(x) when f(c)=g(c)=0.

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