Derivatives Flashcards

1
Q

Derivative of 1/x

A

-1/x^2

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2
Q

Derivative of the square root of x

A

1/(2 • square root of x)

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3
Q

Product Rule:

A

d/dx (u•v) = du • v + u • dv

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4
Q

Quotient Rule:

A

d/dx Hi/Lo = (Lo • dHi - Hi • dLo)/(Lo)^2

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5
Q

Sum Rule:

A

d/dx (u+v) = (du/dx + dv/dx)

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6
Q

Difference Rule:

A

d/dx (u-v) = (du/dx) - (dv/dx)

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7
Q

Derivative of e^x

A

e^x

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8
Q

Derivative of lnx

A

1/x

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9
Q

Power Rule:

A

x^n = nx^n-1

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10
Q

Chain Rule:

A

dy/dx = dy/du • du/dx

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11
Q

Derivative of sinx

A

cosx

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12
Q

Derivative of cosx

A

-sinx

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13
Q

Derivative of tanx

A

sec^2x

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14
Q

Derivative of cscx

A

-cscx • cotx

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15
Q

Derivative of secx

A

secx • tanx

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16
Q

Derivative of cotx

A

-csc^2x

17
Q

d/dx (arcsinx)

A

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

18
Q

d/dx (arccosx)

A

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

19
Q

d/dx (arctanx)

A

1/1 + x^2

20
Q

d/dx (arccotx)

A

-1 /1 + x^2

21
Q

d/dx (arcsecx)

A

1/ |x|•(_/x^2 - 1)

22
Q

d/dx (arccscx)

A

-1/ |x| • (_/x^2 - 1)

23
Q

d/dx logax

A

1/xlna

24
Q

d/dx a^x

A

a^x ln a