Chapter 2

Question 1

f’(x), ln(n)

Answer 1

1/n, x>0

Question 2

f’(x), ln(f(x))

Answer 2

f’/f, f>0

Question 3

lnAB

Answer 3

lnA + lnB

Question 4

ln(A/B)

Answer 4

lnA - lnB

Question 5

lnAⁿ

Answer 5

nlnA

Question 6

[aˣ]’

Answer 6

(lna)aˣ

Question 7

[aᶠ⁽ˣ⁾]’

Answer 7

(lna)aᶠ⁽ˣ⁾ ⋅ f’/x’

Question 8

[logₐx]’

Answer 8

1/(x(lna))

Question 9

[logₐf(x)]’

Answer 9

1/(f(lna)) ⋅ (f’/x’)

Question 10

[sinx]’ chain

Answer 10

cosx ⋅ x’

Question 11

[cosx]’ chain

Answer 11

-sinx ⋅ x’

Question 12

[tanx]’ chain

Answer 12

sec²x ⋅ x’

Question 13

[cotx]’ chain

Answer 13

csc²x ⋅ x’

Question 14

[secx]’ chain

Answer 14

secxtanx ⋅ x’

Question 15

[cscx]’ chain

Answer 15

-cscxcotx ⋅ x’

Question 16

[eˣ]’ chain

Answer 16

eˣ ⋅ x’

Question 17

chain rule

Answer 17

[f(g(x))] → f’(g(x)) ⋅ g’(x)

Question 18

Chain general power rule

Answer 18

[f(x)ⁿ]’ → nxⁿ⁻¹ ⋅ x’

Question 19

constant rule

Answer 19

n’ → 0

Question 20

power rule

Answer 20

[xⁿ]’ → nxⁿ⁻¹

Question 21

constant multiple rule

Answer 21

[c(f(x))]’ → cf’(x)

Question 22

sum and difference rule

Answer 22

[f(x) ± g(x)]’ → f’(x) ± g’(x)

Question 23

[sinx]’

Answer 23

cosx

Question 24

[cosx]’

Answer 24

-sinx

Question 25

natural exponent rule

Answer 25

[eˣ] = eˣ

Question 26

product rule, 2 factors

Answer 26

[f(x) ⋅ g(x)] → fg’ + f’g

Question 27

product rule, 3+ factors

Answer 27

[f ⋅ g ⋅ h…]’ → fgh’ + fg’h + f’gh…

Question 28

quotient rule

Answer 28

[f/g]’ → (gf’ - fg’)/g², g≠0

Question 29

[tanx]’

Answer 29

sec²x

Question 30

[secx]’

Answer 30

secxtanx

Question 31

[cotx]’

Answer 31

-csc²x

Question 32

[cscx]’

Answer 32

-cscxcotx

Question 33

inverse function rule

Answer 33

(f⁻¹)’ = 1/(f’(f⁻¹)), f’(f⁻¹)≠0

Question 34

if P = V, what does “find the rate of change in P w/ respect to V” mean?

Answer 34

It means take the derivative of P & leave behind var V: dP/dV

Question 35

steps in logarithmic differentiation problems

Answer 35

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