Trig Properties & Series & Integrals/Derivatives Flashcards by James Zhang

Q

Derivative of a (constant)

A

0

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Q

Derivative of xⁿ

A

n * x^n-1

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Q

Derivative of e^x

A

e^x

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Q

Derivative of ln(x)

A

1/x

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Q

Derivative of n^x

A

n^x * ln(n)

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Q

Derivative of sin(x)

A

cos(x)

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Q

Derivative of cos(x)

A

-sin(x)

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Q

Derivative of tan(x)

A

sec²(x)

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Q

Derivative of cot(x)

A

-csc²(x)

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Q

Derivative of sec(x)

A

sec(x) * tan(x)

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Q

Derivative of csc(x)

A

-csc(x) * cot(x)

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Q

Derivative of arcsin(x)

A

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Q

Derivative of arccos(x)

A

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Q

Derivative of arctan(x)

A

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Q

Derivative of arccot(x)

A

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Q

Derivative of arcsec(x)

A

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Q

Derivative of arccsc(x)

A

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Q

Integral of 1

A

x + c

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Q

Integral of sin(x)

A

-cos(x) + c

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Q

Integral of cos(x)

A

sin(x) + c

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Q

Integral of tan(x)

A

-ln | cos(x) | + c

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Q

Integral of cot(x)

A

ln | sin(x) | + c

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Q

Integral of sec(x)

A

ln | sec(x) + tan(x) | + c

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Q

Integral of csc(x)

A

-ln | csc(x) + cot(x) | + c

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Q

Integral of sec²(x)

A

tan(x) + c

Q

Integral of csc²(x)

A

-cot(x) + c

Q

Integral of sec(x) * tan(x)

A

sec(x) + c

Q

Integral of csc(x) * cot(x)

A

-csc(x) + c

Q

A

arcsin(x) + c

Q

A

arccos(x) + c

Q

A

arctan(x) + c

Q

A

arccot(x) + c

Q

A

arcsec(x) + c

Q

A

arccsc(x) + c

Q

Derivative of log_b(x)

A

Q

Series of 1 / (1 - x)

A

1 < x < 1

Q

Series of 1 / (1 + x)

A

-1 < x < 1

Q

Series of ln(1 + x)

A

-1 < x <= 1

Q

Series of arctan(x)

A

-1 <= x <= 1

Q

Series of e^x

A

-inf < x < inf

Q

Series of sin(x)

A

-inf < x < inf

Q

Series of cos(x)

A

-inf < x < inf

Q

sin(x)

A

cos(π/2 - x)

Q

sec(x)

A

csc(π/2 - x)

Q

tan(x)

A

cot(π/2 - x)

Q

sin(A + B)

A

sin(A) * cos(B) + sin(B) * cos(A)

Q

cos(A + B)

A

cos(A) * cos(B) - sin(A) * sin(B)

Q

tan(A + B)

A

Q

sin(-x)

A

-sin(x)

ODD

Q

cos(-x)

A

cos(x)

EVEN

Q

tan(-x)

A

-tan(x)

ODD

Q

sin²(x) + cos²(x)

A

1

Q

1 + tan²(x)

Divided original by cos²(x)

A

sec²(x)

Q

sin(2x)

A

2 * sin(x) * cos(x)

Q

tan(2Ø)

A

Q

cos²(x)

A

1 + cos(2x)

2

Q

sin²(x)

A

1 - cos(2x)

2

Q

sin(A) * cos(B)

A

Q

cos(A) * cos(B)

A

Q

sin(A) * sin(B)

A