Derivative Rules Flashcards by Carl Witzel

Q

d/dx(sinx)

A

cosx

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Q

d/dx(cosx)

A

-sinx

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Q

d/dx(tanx)

A

(secx)^2

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Q

d/dx(secx)

A

secx(tanx)

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Q

d/dx(cscx)

A

-cscx(cotx)

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Q

d/dx(cotx)

A

-(cscx)^2

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Q

d/dx[f(g(x))]

A

f’(g(x))g’(x)

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Q

d/dx(e^x)

A

e^x

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Q

d/dx(lnx)

A

1/x

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Q

d/dx(log base a of x)

A

1/(xlna)

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Q

d/dx(a^x)

A

a^x(lna)

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Q

d/dx(sin^-1(x))

A

1/((1-x^2)^1/2)

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Q

d/dx(cos^-1(x))

A

-1/((1-x^2)^1/2)

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Q

d/dx(tan^-1(x))

A

1/(1+x^2)

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Q

d/dx(sec^-1(x))

A

1/(|x|((x^2-1)^1/2)

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Q

d/dx(csc^-1(x))

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A

-1/(|x|((x^2-1)1/2)

Q

d/dx(cot^-1(x))

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A

-1/(1+x^2)

Q

(f^-1)’(b)

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A

1/(f’(f^-1(b)))