Chapter 2 Flashcards
1
Q
f’(x), ln(n)
A
1/n, x>0
2
Q
f’(x), ln(f(x))
A
f’/f, f>0
3
Q
lnAB
A
lnA + lnB
4
Q
ln(A/B)
A
lnA - lnB
5
Q
lnAⁿ
A
nlnA
6
Q
[aˣ]’
A
(lna)aˣ
7
Q
[aᶠ⁽ˣ⁾]’
A
(lna)aᶠ⁽ˣ⁾ ⋅ f’/x’
8
Q
[logₐx]’
A
1/(x(lna))
9
Q
[logₐf(x)]’
A
1/(f(lna)) ⋅ (f’/x’)
10
Q
[sinx]’ chain
A
cosx ⋅ x’
11
Q
[cosx]’ chain
A
-sinx ⋅ x’
12
Q
[tanx]’ chain
A
sec²x ⋅ x’
13
Q
[cotx]’ chain
A
csc²x ⋅ x’
14
Q
[secx]’ chain
A
secxtanx ⋅ x’
15
Q
[cscx]’ chain
A
-cscxcotx ⋅ x’
16
Q
[eˣ]’ chain
A
eˣ ⋅ x’
17
Q
chain rule
A
[f(g(x))] → f’(g(x)) ⋅ g’(x)
18
Q
Chain general power rule
A
[f(x)ⁿ]’ → nxⁿ⁻¹ ⋅ x’
19
Q
constant rule
A
n’ → 0
20
Q
power rule
A
[xⁿ]’ → nxⁿ⁻¹
21
Q
constant multiple rule
A
[c(f(x))]’ → cf’(x)
22
Q
sum and difference rule
A
[f(x) ± g(x)]’ → f’(x) ± g’(x)
23
Q
[sinx]’
A
cosx
24
Q
[cosx]’
A
-sinx
25
natural exponent rule
[eˣ] = eˣ
26
product rule, 2 factors
[f(x) ⋅ g(x)] → fg' + f'g
27
product rule, 3+ factors
[f ⋅ g ⋅ h...]' → fgh' + fg'h + f'gh...
28
quotient rule
[f/g]' → (gf' - fg')/g², g≠0
29
[tanx]'
sec²x
30
[secx]'
secxtanx
31
[cotx]'
-csc²x
32
[cscx]'
-cscxcotx
33
inverse function rule
(f⁻¹)' = 1/(f'(f⁻¹)), f'(f⁻¹)≠0
34
if P = V, what does "find the rate of change in P w/ respect to V" mean?
It means take the derivative of P & leave behind var V: dP/dV
35
steps in logarithmic differentiation problems
1)
