derivatives & integrals review Flashcards
d/dx [u +/- v] =
u’ +/- v’
d/dx [cu] =
cu’
d/dx [uv] =
uv’ + vu’
firstDsecond + secondDfirst
d/dx [u/v] =
(vu’ - uv’) / v^2
loDhi - hiDlo / (lo)^2
d/dx [c] =
0
c is a constant
d/dx [u^n] =
nu^n-1(u’)
power rule
d/dx [x] =
1
x has a power of one, so 1
d/dx [ln u] =
u’ / u
d/dx [e^u] =
e^u (u’)
d/dx [sin u] =
(cos u) u’
d/dx [cos u] =
- (sin u) u’
(negative sin u)
d/dx [tan u] =
(sec^2 u) u’
d/dx [cot u] =
- (csc^2 u) u’
negative (csc^2 u) u’
d/dx [sec u] =
(sec u tan u) u’
d/dx [csc u] =
- (csc u cot u) u’
∫ k f(u) du =
k ∫ f(u) du
∫ [f(u) +/- g(u)] du =
∫ f(u) du +/- ∫ g(u) du
∫ du =
u + C
∫ sin u du =
- cos u + C
∫ cos u du =
sin u + C
∫ sec^2 u du =
tan u + C
∫ csc^2 u du =
- cot u + C
∫ sec u tan u du =
sec u + C
∫ csc u cot u du =
- csc u + C
∫ a^u du =
(1/ln a) a^u + C
∫ tan u du =
-ln |cos u| + C
∫ sec u du =
ln |sec u + tan u|+ C
∫ du / (a^2 + u^2) =
1/a arctan u/a + C
∫ du / sqrt (a^2 - u^2) =
arcsin u/a + C
∫ du/ u ( sqrt (u^2 - a^2))
1/arcsec (|u|/a) + C
∫ csc u du =
-ln |cscu + cotu| + C
