Unit 1 Properties Flashcards by Mitch Parker | Brainscape

Q

1/sinx =

A

cscx

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Q

1/cosx

A

secx

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Q

1/tanx

A

cotx

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Q

pythag for sin

A

sin^2x+cos^2x=1

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Q

pythag for tan

A

1+tan^2x=sec^2x

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Q

pythag for cot

A

1+cot^2x=csc^2x

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Q

pythag for cos

A

sin^2x+cos^2x=1

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Q

pythag for sec

A

1+tan^2x=sec^2x

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Q

pythag for csc

A

1+cot^2x=csc^2x

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Q

d/dx(lnx) =

A

1/x for x>0

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Q

d/dx(log sub b of x) =

A

1/xlnb for x>0

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Q

d/dx(b^x) =

A

b^x * lnb

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Q

d/dx(secx) =

A

secx * tanx

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Q

d/dx(cscx) =

A

MINUS cscx * cotx

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Q

d/dx(tanx) =

A

sec^2x

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Q

d/dx(cotx) =

A

MINUS csc^2x

Q

d/dx(sin^-1x) =

A

1 / root(1-x^2)
* or negative cos^-1

Q

d/dx(cos^-1x) =

A

MINUS 1 / root(1-x^2)
* or negative sin^-1

Q

d/dx(tan^-1x) =

A

1 / (1+x^2)
* or sin^-1/cos^-1 without root

Q

d/dx(cot^-1x) =

A

MINUS 1 / (1+x^2)
* or negative tan^-1

Q

derivative product rule

A

left d,right + right d,left

Q

derivative quotient rule

A

low d,high - high d,low / low^2

Q

d/dx(f(g(x))) chain rule

A

fprime(g(x)) * gprime(x)

Q

∫(1/x)dx =

A

ln|x| + C

Q

∫sec^2xdx =

A

tanx + C

Q

∫csc^2xdx

A

MINUS cotx + C

Q

∫secx * tanx dx =

A

secx + C

Q

∫cscx * cotx dx =

A

MINUS cscx + C

Q

∫b^x dx =

A

(1/lnb) * b^x + C

Q

∫log sub b of x dx

A

(1/lnb) * ∫lnxdx

Q

∫tanxdx =

A

MINUS ln|cosx| + C

Q

∫cotxdx =

A

ln|sinx| + C

Q

∫secxdx =

A

ln|secx + tanx| + C

Q

∫cscxdx =

A

ln|cscx - cotx| + C

Q

washer method

A

V = pi * a to b∫ (bigr^2 - smallr^2)dx

Q

1/cscx =

A

sinx

Q

1/secx =

A

cosx

Q

1/cotx =

A

tanx