λ

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´ؿ f(x) ˤĤƶ˸

\[ \lim_{x \to a} {f(x) - f(a) \over x - a}= \lim_{\Delta x \to 0} {f(a+\Delta x) - f(a) \over \Delta x} , (x = a + \Delta x) \]

¸ߤȤ f(x) x = a ˤʬǽ(differentiable)Ǥȸޤ ζ˸¤ f(a) Ƚ x = a ˤ f(x) ʬȸޤ

\[(x^{a})′ = ax^{a−1}\]

\[(sin x)′ = cos x\]

\[(cos x)′ = −sin x\]

\[ (\tan x)' = {1 \over \cos^2 x} = 1 + \tan^2 x \]

\[(\arcsin x)'= {1 \over \sqrt{1-x^2}} \]

\[(\arccos x)'= -{1 \over \sqrt{1-x^2}} \]

\[(\arctan x)'= {1 \over 1+x^2} \]

\[(e^{x})′ = e^{x}\]

\[(a^{x})′ = log(a) a^{x}\]

\[(\log x)'= {1 \over x} \]

\[(\log_a x)'= {1 \over x \log a} \]



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Last-modified: 2008-11-17 () 18:00:05 (4039d)