AP Calc Quiz 3 Notes

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Calculus

Derivatives & Differentiation

Last updated 7:27 PM on 9/23/26
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8 Terms

1
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ddxf(g(x))\frac{d}{dx}f\left(g\left(x\right)\right)

f′(g(x))⋅g′(x)f^{\prime}\left(g\left(x\right)\right)\cdot g^{\prime}\left(x\right)

2
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ddxf−1(u)\frac{d}{dx}f^{-1}\left(u\right)

u′f′(f−1(u))\frac{u^{\prime}}{f^{^{\prime}}\left(f^{-1}\left(u\right)\right)}

3
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ddxsin⁡−1(u)\frac{d}{dx}\sin^{-1}\left(u\right)

u′1−u2\frac{u^{\prime}}{\sqrt{1-u^2}}

4
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ddxtan⁡−1(u)\frac{d}{dx}\tan^{-1}\left(u\right)

u′1+u2\frac{u^{\prime}}{1+u^2}

5
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ddxsec⁡−1(u)\frac{d}{dx}\sec^{-1}\left(u\right)

u′∣u∣u2−1\frac{u^{\prime}}{\left|u\right|\sqrt{u^2-1}}

6
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ddxlog⁡a(u)\frac{d}{dx}\log_{a}\left(u\right)

u′u⋅ln⁡(a)\frac{u^{\prime}}{u\cdot\ln\left(a\right)}

7
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ddxln⁡(u)\frac{d}{dx}\ln\left(u\right)

u′u\frac{u^{\prime}}{u}

8
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ddxau\frac{d}{dx}a^{u}

lna⋅au⋅u′lna\cdot a^{u}\cdot u^{\prime}