Differentiation Flashcards

1
Q

xⁿ

A

nxⁿ⁻¹

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2
Q

(ax+b)ⁿ

A

na(ax+b)ⁿ⁻¹

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3
Q

A

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4
Q

eᵃˣ⁺ᵇ

A

aeᵃˣ⁺ᵇ

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5
Q

lnx

A

1/x

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6
Q

ln(ax+b)

A

a/ ax+b

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7
Q

sinx

A

cosx

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8
Q

cosx

A

-sinx

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9
Q

tanx

A

sec²x

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10
Q

secx

A

secxtanx

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11
Q

cosecx

A

-cosecxcotx

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12
Q

cotx

A

-cosec²x

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13
Q

sin⁻¹x

A

1/√1-x²

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14
Q

cos⁻¹x

A

-1/√1-x²

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15
Q

tan⁻¹x

A

1/1+x²

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16
Q

product rule y=uv

A

dy/dx= u dv/dx + v du/dx

17
Q

quotient rule y=u/v

A

dy/dx (v du/dx - u dv/dx)/v²

18
Q

chain rule

A

dy/dx= dy/du by du/dx

19
Q

reciprocal rule

A

1/f(x)= f’(x)/(f(x))²