differentiation & integration REVIEW Flashcards
d/dx [cu] =
cu’
d/dx [u/v] =
vu’ - uv’ / v^2
d/dx [x] =
1
d/dx [e^u] =
e^u * u’
d/dx [sin u] =
(cos u)u’
d/dx [cot u] =
-(csc^2 u) u’
d/dx [arcsin u] =
u’ / ( sqrt (1-u^2))
d/dx [arccot u]=
-u’ / (1+u^2)
d/dx [u +/- v] =
u’ +/- v’
d/dx [c] =
0
d/dx [log(base a) u] =
u’ / (ln a) u
d/dx [cos u] =
-(sin u) u’
d/dx [arccos u] =
-u’ / (sqrt (1-u^2))
{same as arcsin u, but neg}
d/dx [arcsec u] =
u’ / (|u| (sqrt (u^2 -1))
d/dx [uv] =
uv’ + vu’
d/dx [u^n] =
power rule =
nu^(n-1) (u’)
d/dx [ln u] =
u’ / u
d/dx [a^u]
(ln a)a^u (u’)
d/dx [tan u] =
(sec^2 u)u’
d/dx [csc u] =
- (csc u cot u)u’
d/dx [sec u] =
(sec u tan u)u’
d/dx [arctan u] =
u’ / (1+u^2)
d/dx [arcsec u] =
NEG (u’ / (|u| (sqrt (u^2 -1)) )
∫ k f(u) du =
k ∫f(u) du
∫ du =
u + C
∫e^u du =
e^u + C
∫cos u du =
sin u + C
∫cot u du =
ln |sin u| + C
∫csc u du =
-ln|csc u + cot u| + C
∫csc^2 u du =
-cot u + C
∫ cscu cotu du =
-csc u + C
∫du / a^2 + u^2 =
1/a arctan u/a + C
∫ [f(u) +/- g(u)] du =
∫ f(u) du +/- ∫ g(u) du
∫a^u du
(1/ln a) a^u + C
∫ sinu du =
-cos u + C
∫ tanu du =
-ln |cos u| + C
∫secu du =
ln |sec u + tan u| + C
∫ sec^2 u du =
tan u + C
∫ sec u tan u du =
sec u + C
∫ du / (sqrt (a^2 - u^2))
arcsin u/a + C
∫du / (u (sqrt (u^2 - a^2))
1/a arcsec |u|/a + C
