Chapter 2 Flashcards
f’(x), ln(n)
1/n, x>0
f’(x), ln(f(x))
f’/f, f>0
lnAB
lnA + lnB
ln(A/B)
lnA - lnB
lnAⁿ
nlnA
[aˣ]’
(lna)aˣ
[aᶠ⁽ˣ⁾]’
(lna)aᶠ⁽ˣ⁾ ⋅ f’/x’
[logₐx]’
1/(x(lna))
[logₐf(x)]’
1/(f(lna)) ⋅ (f’/x’)
[sinx]’ chain
cosx ⋅ x’
[cosx]’ chain
-sinx ⋅ x’
[tanx]’ chain
sec²x ⋅ x’
[cotx]’ chain
csc²x ⋅ x’
[secx]’ chain
secxtanx ⋅ x’
[cscx]’ chain
-cscxcotx ⋅ x’
[eˣ]’ chain
eˣ ⋅ x’
chain rule
[f(g(x))] → f’(g(x)) ⋅ g’(x)
Chain general power rule
[f(x)ⁿ]’ → nxⁿ⁻¹ ⋅ x’
constant rule
n’ → 0
power rule
[xⁿ]’ → nxⁿ⁻¹
constant multiple rule
[c(f(x))]’ → cf’(x)
sum and difference rule
[f(x) ± g(x)]’ → f’(x) ± g’(x)
[sinx]’
cosx
[cosx]’
-sinx
natural exponent rule
[eˣ] = eˣ
product rule, 2 factors
[f(x) ⋅ g(x)] → fg’ + f’g
product rule, 3+ factors
[f ⋅ g ⋅ h…]’ → fgh’ + fg’h + f’gh…
quotient rule
[f/g]’ → (gf’ - fg’)/g², g≠0
[tanx]’
sec²x
[secx]’
secxtanx
[cotx]’
-csc²x
[cscx]’
-cscxcotx
inverse function rule
(f⁻¹)’ = 1/(f’(f⁻¹)), f’(f⁻¹)≠0
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
steps in logarithmic differentiation problems
1)
