Calculus · AP · Test Prep

AP 微積分公式

AP 微積分 AB/BC 的導數、積分與級數公式填空卡。

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導數的冪次法則：d/dx(x^n) = ____

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n·x^(n-1)

乘積法則：d/dx(u·v) = ____

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u'·v + u·v'

商法則：d/dx(u/v) = ____

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(u'·v - u·v')/v²

連鎖律：d/dx[f(g(x))] = ____

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f'(g(x))·g'(x)

d/dx(sin x) = ____

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cos x

d/dx(cos x) = ____

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-sin x

d/dx(tan x) = ____

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sec²x

d/dx(cot x) = ____

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-csc²x

d/dx(sec x) = ____

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sec x·tan x

d/dx(csc x) = ____

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-csc x·cot x

d/dx(e^x) = ____

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e^x

d/dx(ln x) = ____

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1/x

d/dx(a^x) = ____

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a^x·ln a

d/dx(arcsin x) = ____

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1/√(1-x²)

d/dx(arctan x) = ____

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1/(1+x²)

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