Chapter 6 Flashcards by Martin Hernandez

Q

Hyperbolic cosine

A

(e^x + e^-x) / 2

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Q

Hyperbolic sine

A

(e^x - e^-x) / 2

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Q

Hyperbolic tangent

A

(sinhx / coshx ) = (e^x - e^-x) / (e^x + e^-x)

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Q

Hyperbolic cotangent

A

(coshx / sinhx) = (e^x + e^-x) / (e^x - e^-x)

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Q

Hyperbolic secant

A

(1 / coshx) = 2 / (e^x + e^-x)

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Q

Hyperbolic cosecant

A

(1 / sinhx) = 2 / (e^x - e^-x)

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Q

1 =

A

cosh^2(x) - sinh^2(x)

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Q

cosh(-x)

A

cosh x

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Q

sinh (-x)

A

sinh x

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Q

tanh (-x)

A

tanh x

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Q

cosh (x + y)

A

coshx coshy + sinhx sinhy

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Q

sinh (x + y)

A

sinhx coshy + coshx sinhy

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Q

cosh 2x

A

cosh^2(x) + sinh^2(x)

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Q

sinh 2x

A

2sinh(x)cosh(x)

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Q

cosh^2 (x)

A

(cosh(2x) + 1) / 2

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Q

sinh^2 ( x )

A

(cosh(2x) - 1) / 2

Q

sech^2(x)

A

1 - tanh^2(x)

Q

csch^2(x)

A

coth^2(x) - 1

Q

derivative of coshx

A

sinhx

Q

derivative of sinhx

A

coshx

Q

derivative of tanhx

A

sech^2(x)

Q

derivative of cothx

A

-csch^2(x)

Q

derivative of sechx

A

-sech(x)tanh(x)

Q

derivative of cschx

A

-csch(x)coth(x)

Q

intergral of sinh(x)dx

A

coshx + C

Q

integral of cosh(x)dx

A

sinhx + C

Q

intergral of sech^2(x)dx

A

tanhx + C

Q

integral of csch^2(x)dx

A

-cothx + C

Q

intergral of sech(x)tan(x)dx

A

-sechx + C

Q

intergral of csch(x)coth(x)dx

A

–cschx + C

Q

intergral of tanh(x)dx

A

ln cosh(x) + C

Q

intergral of coth(x)dx

A

ln |sinh(x)| + C

Q

intergral of sech(x)dx

A

arctan(sinhx) + C

Q

intergral of csch(x)dx

A

ln | tanh(x / 2) | + C