Derivatives Flashcards by Eliza Dixon | Brainscape

Q

Y=sinx

A

Y’ =cosx

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Q

Y=cosx

A

Y’= -sinx

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Q

Y=tanx

A

Y’= sec^2x

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Q

Y=cotx

A

Y’= -csc^2x

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Q

Y=secx

A

Y’=secxtanx

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Q

Y=cscx

A

Y’= -cscxcotx

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Q

Product rule

A

Y’=f (x)g’(x)+g(x)f’(x)

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Q

Quotient rule

A

Y’= (g(x)f’(x) - f(x)g’(x))/((g(x))^2)

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Q

y=lnx

A

y’=1/x

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Q

Y=logbX

A

Y’= 1/(xlnb)

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Q

Y=b^x

A

Y’=b^xlnb

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Q

Y=e^x

A

Y’=e^x

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Q

Y=e^-x

A

Y’= -e^-x

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Q

Sqrt(x)

A

1/(2sqrtx)

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Q

Y=arcsinx

A

y’=1/(sqrt(1-x^2))

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Q

Y=arccosx

A

Y’= -1/(sqrt(1-x^2))

Q

Y=arctanx

A

Y’=1/(1+x^2)

Q

Y=arccotx

A

Y’=-1/(1+x^2)

Q

Y=arcsecx

A

Y’=1/(|x|sqrt(x^2-1))

Q

Y=arccscx

A

Y’=-1/(|x|sqrt(x^2-1))

Q

Sinhx

A

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

Q

Coshx

A

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

Q

Cosh^2-sinh^2x=

A

=1

Q

Y=sinhx

A

Y’=coshx

Q

Y=coshx

A

Y’=sinhx

Q

Y=tanhx

A

Y’=sech^2x

Q

Y=cothx

A

Y’=-csch^2x

Q

Y=sechx

A

Y’=-tanhxsechx

Q

Y=cschx

A

Y’=-cothxcschx

Q

Y=arcsinhx

A

Y’=1/(sqrt(1+x^2))

Q

Y=arctanhx

A

Y’=1/(1-x^2)