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Hint

1

t/f: if a function is differentiable then it is continuous

true

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2

t/f: if continuous then differentiable

false

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3

t/f: if a function is NOT continuous then NOT differentiable

True

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4

t/f: if NOT differentiable then NOT continuous

false

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5

what graphical features make a function not differentiable

a cusp/sharp corner, a discontinuity, vertical tangent (steep downward hill)

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6

d/dx(sinx)

cosx

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7

d/dx(cosx)

-sinx

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8

d/dx(tanx)

secÂ˛x

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9

d/dx(cotx)

-cscÂ˛x

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10

d/dx(secx)

(secx)(tanx)

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11

d/dx(cscx)

-csc(x)cot(x)

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12

d/dx sqrt(x)

1/2sqrt(x)

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13

d/dx e^x

e^x

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14

d/dx lnx

1/x

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15

d/dx b^x

(b^x)(lnb)

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16

d/dx logb(x)

1/(x)(lnb)

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17

AROC equation

y2-y1/x2-x1

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18

definition of a derivative at a point

fâ€™(c)=limxâ†’c f(x)-f(c)/x-c

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19

definition of a derivative as a function

fâ€™(x)= lim hâ†’0 f(x+h)-f(x)/h

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20

power rule definition if f(x)=ax^n

fâ€™(x)=(nâ€˘a)x^n-1

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21

power rule example: 3xÂł

9xÂ˛

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22

product rule definition if h(x)=f(x)â€˘g(x)

hâ€™(x)=fâ€™(x)â€˘g(x)+f(x)â€˘gâ€™(x)

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23

product rule example (3xÂ˛)(sinx)

6xâ€˘sinx+3xÂ˛â€˘cosx

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24

quotient rule if h(x)=f(x)/g(x)

hâ€™(x)=fâ€™(x)â€˘g(x)-f(x)â€˘gâ€™(x)/g(x)Â˛

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25

chain rule definition if h(x)=f(g(x))

hâ€™(x)=fâ€™(g(x))â€˘gâ€™(x)

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26

chain rule example: sinÂ˛x

2(sinx)â€˘cosx

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27

quotient rule example xÂ˛/5x

2xâ€˘5x-xÂ˛â€˘5/5xÂ˛

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