Derivatives Flashcards

1
Q

sin(x)

A

cos(x)

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2
Q

cos(x)

A

-sin(x)

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3
Q

tan(x)

A

sec^2(x)

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4
Q

csc(x)

A

-csc(x)cot(x)

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5
Q

sec(x)

A

sec(x)tan(x)

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6
Q

cot(x)

A

-csc^2(x)

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7
Q

sin^-1(f(x))

A

f’(x)/(sqrt(1-f(x)^2))

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8
Q

cos^-1(f(x))

A

-f’(x)/(sqrt(1-f(x)^2))

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9
Q

tan^-1(f(x))

A

f’(x)/(1+f(x)^2)

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10
Q

ln(x)

A

1/x

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11
Q

csc^-1(f(x))

A

-f’(x)/(|f(x)|(f(x)^2-1)^(1/2))

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12
Q

sec^-1(f(x))

A

f’(x)/(|f(x)|(f(x)^2-1)^(1/2))

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13
Q

cot^-1(f(x))

A

-f’(x)/(1+f(x)^2)

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14
Q

e^x

A

e^x

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15
Q

a^x

A

lna(a^x)

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16
Q

f(x)/g(x)

A

(f’(x)g(x)-f(x)g’(x))/g(x)^2