Calculus Derivatives/Antiderivatives

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AP Calc

Last updated 3:10 PM on 4/12/26
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35 Terms

1
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d/dx (n)

0

2
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d/dx (x)

1

3
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d/dx (xⁿ)

nxⁿ⁻¹ (power rule)

4
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d/dx eˣ

eˣ

5
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d/dx (lnx)

1/x

6
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d/dx nˣ

nˣ(lnx)

7
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d/dx sinx

cosx

8
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d/dx cosx

−sinx

9
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d/dx tanx

sec²x

10
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d/dx cotx

-csc²x

11
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d/dx secx

secxtanx

12
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d/dx cscx

-cscxcotx

13
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d/dx sin⁻¹x

1/ √(1-x²)

14
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d/dx cos⁻¹x

-1/ √(1-x²)

15
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d/dx tan⁻¹x

1/(1+x²)

16
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d/dx cot⁻¹x

-1/(1+x²)

17
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d/dx sec⁻¹x

1/ |x|√(x²-1)

18
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d/dx csc⁻¹x

-1/ |x|√(x²-1)

19
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∫ 1 dx

x + C

20
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∫ xⁿ dx

(xⁿ⁺¹)/(n+1) + C

21
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∫ eˣ dx

eˣ + C

22
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∫ (1/x) dx

ln|x| + C, x≠0

23
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∫ nˣ dx

nˣ/(ln|n|) + C

24
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∫ cosx dx

sinx + C

25
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∫ sinx dx

-cosx + C

26
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∫ sec²x dx

tanx + C

27
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∫ csc²x dx

-cotx + C

28
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∫ secxtanx dx

secx + C

29
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∫ cscxcotx dx

-cscx + C

30
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∫ 1/√(1-x²) dx

sin⁻¹x + C

31
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∫ -1/√(1-x²) dx

cos⁻¹x + C

32
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∫ 1/(x²+1) dx

tan⁻¹x + C

33
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∫ -1/(1+x²) dx

cot⁻¹x + C

34
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∫ 1/ |x|√(x²-1) dx

sec⁻¹x + C

35
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∫ -1/ |x|√(x²-1) dx

csc⁻¹x + C