CALC BC- Derivatives

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Average Rate of Change

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18 Terms

1

Average Rate of Change

Slope (f(b)-f(a))/(b-a)

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2

Instantaneous Rate of Change

as the limit approaches c, (f(x)-f©)/(f-c)

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3

Limit Definition of the Derivative

As the limit of h approaches 0, (f(x+h)-f(x))/h

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4

sin²x+cos²x

=1

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5

sin(x+y)

=sinxcosy+cosxsiny

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6

cos(x+y)

cosxcosy-sinxsiny

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7

Tangent Line of a graph of f at x=c

y-f©=f’©(x-c)

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8

A line normal (perpendicular) to the graph of f at x=c

y-f©=(-1/f’©)(x-c)

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9

Derivative of a Constant

0

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10

Power Rule—→ x^n=

nx^(n-1)

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11

Exponential Base e^x=

e^x

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12

Logarithmic base lnx=

1/x

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13

Derivative of sinx=

cosx

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14

Derivative of tanx

sec²x

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15

Derivative of secx

secxtanx

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16

Derivative of cosx

-sinx

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17

Derivative of cotx

-csc²x

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18

Derivative of cscx

-cscxcotx

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