Derivatives + Anti-derivatives to Memorize for Calc

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Derivatives + anti-derivatives of trig + logarithmic functions. Good for Calc 🤩 For the purpose of the flashcards, integrals/anti-derivatives are denoted by the { symbol, and derivatives by d/dx.

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21 Terms

1
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d/dx(sin(x))

cos(x)

2
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d/dx(cos(x))

-sin(x)

3
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d/dx(tan(x))

sec²(x)

4
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d/dx(cot(x))

-csc²(x)

5
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{cos(x)dx

sin(x)+C

6
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{sin(x)dx

-cos(x)+C

7
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{sec²(x)dx

tan(x)+C

8
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{csc²(x)

-cot(x)+C

9
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{sec(x)tan(x)dx

sec(x)+C

10
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{csc(x)cot(x)dx

-csc(x)+C

11
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d/dx(e^kx)

ke^kx

12
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d/dx(lnx)

1/x

13
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{(e^kx)dx

(1/k)e^kx+C

14
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{(1/x)dx

lnx+C

15
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d/dx(lnx)

xln(x)-x+C

16
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d/dx(sin^-1x)

1/(1-x²)^1/2

17
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d/dx(cos^-1x)

-1/(1-x²)^1/2

18
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d/dx(tan^-1x)

1/(1+x²)

19
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d/dx(sec^-1x)

1/(x(x²-1)^1/2

20
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d/dx(csc^-1x)

-1/(x(x²-1)^1/2

21
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d/dx(cot^-1x)

-1/(x²+1)