midterm 2

Question 1

Product rule [f(x)g(x)}

Answer 1

f(x)g’(x)+g(x)f’(x)

Question 2

Quotient rule [f(x)/g(x)]

Answer 2

g(x)f’(x)-f(x)g’(x)/g(x)^2

Question 3

Power rule [x^n]

Answer 3

nx^n-1

Question 4

Difference rule [f(x)-g(x)]

Answer 4

f’(x)-g’(x)

Question 5

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

Answer 5

f’(g(x))g’(x)

Question 6

Constant multiple [g(x) = C*f(x)]

Answer 6

C*f’(x)

Question 7

Sum rule [f(x)+g(x)]

Answer 7

f’(x)+g’(x)

Question 8

sinx

Answer 8

cosx

Question 9

cosx

Answer 9

-sinx

Question 10

tanx

Answer 10

sec^2x

Question 11

secx

Answer 11

secxtanx

Question 12

cotx

Answer 12

-csc^2x

Question 13

cscx

Answer 13

-cscxcotx

Question 14

tanx (identity)

Answer 14

sinx/cosx

Question 15

sin(ax)

Answer 15

acos(ax)

Question 16

cos(ax)

Answer 16

-asin(ax)

Question 17

a^x

Answer 17

ln(a)a^x

Question 18

e^x

Answer 18

e^x

Question 19

e^kx

Answer 19

ke^x

Question 20

lnx

Answer 20

1/x

Question 21

sin^-1x

Answer 21

1/sqrt(1-x^2)

Question 22

cos^-1x

Answer 22

-1/sqrt(1-x^2)

Question 23

tan^-1x

Answer 23

1/1+x^2

Question 24

cot^-1x

Answer 24

-1/1+x^2

Question 25

sec^-1x

Answer 25

1/xsqrt(x^2-1)

Question 26

csc^-1x

Answer 26

-1/xsqrt(x^2-1)

Question 27

How do you find critical numbers?

Answer 27

set f’(x) = 0 and solve

Question 28

how do you find where f(x) is increasing/decreasing?

Answer 28

evaluate f’(x) at intervals

Question 29

how do you find inflection points?

Answer 29

set f’‘(x) = 0 and solve

Question 30

How do you find relative extrema?

Answer 30

evaluate f(x) at increasing and decreasing intervals

Question 31

how do you find absolute extrema?

Answer 31

evaluate f(x) at all intervals

Question 32

l’Hospitals rule

Answer 32

if f(x)/g(x) = 0/0 or oo/oo the f’(x)/g’(x)

Question 33

how do you find delta x?

Answer 33

b-a/n

Question 34

What is the derivative of position?

Answer 34

velocity

Question 35

What is the derivative of velocity?

Answer 35

acceleration