formula to know Flashcards by pen 6816 | Brainscape

Q

Express log_ax in terms of log_b

A

log_bx/ log_ba

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Q

sinh 2x

A

2*sinh(x)*cosh(x)

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Q

cosh(2x)

A

cosh²(x) + sinh²(x)

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Q

quotient rule

A

y=u/v

(v*u’-u*v’)/v²

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Q

intergration by parts

A

∫u*v’=u*v-∫v*u’

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Q

diff of tan kx

A

ksec² kx

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Q

diff of sec x

A

sec x * tan x

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Q

diff of cot x

A

-cosec²x

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Q

diff of cosec x

A

-cosec x * cot x

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Q

diff of arcsin x

A

1/ (1-x²)^0.5

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Q

diff of arc cos(x)

A

-1/ (1-x²)^0.5

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Q

diff of arctan(x)

A

1 / 1+x²

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Q

diff of tanh(x)

A

sech²(x)

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Q

diff of arsinh(x)

A

1 / (1+x²)^0.5

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Q

diff of arcosh (x)

A

1 / (x²-1)^0.5

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Q

diff of artanh(x)

A

1 / (1-x²)

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Q

∫sec²kx

A

(1/k) tan(kx)

Q

∫tan x

A

ln |sec x|

Q

∫ cot(x)

A

ln |sin x|

Q

∫tanh x

A

ln (coshx)

Q

What links together cosh and sinh?

A

cosh²-sinh²=1

Q

What is sinh(2x) equal to?

A

2*sinh(x)*cosh(x)

Q

cosh(2x)=

A

sinh²(x)+cosh²(x)

Q

log_aX=

A

log_bX/log_ba

Q

ksec² kx

A

diff of tan kx

Q

sec x * tan x

A

diff of sec x

Q

-cosec²x

A

diff of cot x

Q

-cosec x * cot x

A

diff of cosec x

Q

1/ (1-x²)^0.5

A

diff of arcsin x

Q

-1/ (1-x²)^0.5

A

diff of arc cos(x)

Q

1 / 1+x²

A

diff of arctan(x)

Q

sech²(x)

A

diff of tanh(x)

Q

1 / (1+x²)^0.5

A

diff of arsinh(x)

Q

1 / (x²-1)^0.5

A

diff of arcosh (x)

Q

1 / (1-x²)

A

diff of artanh(x)

Q

arcsin(x)=

A

-arcsin(-x)

Q

arcos(x)

A

π-arcos(-x)

Q

arctan(x)

A

-arctan(-x)

Q

what is root i?

A

1/√2 + 1/√2i

Q

A