AP Calc- Derivatives

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d/dx [arcsin u]

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1

d/dx [arcsin u]

u’ / sqrt(1-u²)

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2

d/dx [arctan u]

u’ / 1 + u²

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3

d/dx [arcsec u]

u’ / |u| sqrt(1-u²)

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4

d/dx [arcsin (u/a)]

u’ / sqrt(a² - u²)

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5

d/dx [arctan (u/a)]

(a)(u’ ) / a² + u²

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6

d/dx [tan x]

sec² x

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7

d/dx [cot x]

-csc² x

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8

d/dx [sec x]

sec x tan x

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9

csc x

-csc x cot x

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10

d/dx [x² + y² ]

2x + 2y (dy/dx)

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11

d/dx [ xy ]

(1)(y) + (dy/dx) (x)

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12

d/dx [ x² * ln x ]

(2x)(ln x) + (1/x)(x²)

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13

d/dx [ e^x sec x ]

(e^x)(sec x) + (sec x tan x) (e^x)

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14

d/dx [ 3^sqrt(x-2) ]

( (3^sqrt(x-2)) (ln 3) ) (1/(2)(sqrt(x-2)) )

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15

d/dx [ cos^4 (6x) ]

(4(cos³(6x)) (-sin (6x) (6))

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16

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

f’(x) + g’(x)

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17

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

(f’(x))(g(x)) + (g’(x)) (f(x))

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18

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

( (f’(x))(g(x)) - (g’(x))(f(x)) ) / g(x)²

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19

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

f’(g(x)) (g’(x))

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20

d/dx [ sqrt(x) ]

1 / 2 sqrt(x)

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