Differentiation and Integration Formulas Flashcards
d(cu)
cu’
d(u ± v)
u’ ± v’
d(uv)
uv’ + vu’
d(u/v)
(vu’ - uv’)/v^2
d(c)
0
d(u^n)
n(u^(n-1))(u’)
d(x)
1
d(abs(u))
u/abs(u) * (u’), u ≠ 0
d(ln(u))
u’/u
d(e^u)
(e^u)u’
d(log(bs(a))u)
u’/(ln(a))u
d(a^u)
(ln(a))(a^u)(u’)
d(sin(u))
(cos(u))(u’)
d(cos(u))
-(sin(u))(u’)
d(tan(u))
(sec^2(u))(u’)
d(cot(u))
-(csc^2(u))(u’)
d(sec(u))
(sec(u)*tan(u))(u’)
d(csc(u))
-(csc(u)*cot(u))(u’)
d(arcsin(u))
u’/sqrt(1 - (u^2))
d(arctan(u))
u’/(1+(u^2))
∫kf(u)(du)
k∫f(u)(du)
∫f(u)(du) ± ∫g(u)(du)
∫(du)
u + C
∫(u^n)(du)
[(u^(n+1))/(n + 1)] + C, n ≠ -1
∫(du)/u
ln(abs(u)) + C
∫(e^u)(du)
(e^u) + C
∫(a^u)(du)
[1/(ln(a)) * (a^u)] + C
∫sin(u)(du)
-cos(u) + C
∫cos(u)(du)
sin(u) + C
∫tan(u)(du)
-ln(abs(cos(u))) + C
∫cot(u)(du)
ln(abs(sin(u))) + C
∫sec(u)(du)
ln(abs(sec(u) + tan(u))) + C
∫csc(u)(du)
-ln(abs(csc(u) + cot(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
∫(du)/sqrt((a^2) - (u^2))
arcsin(u/a) + C
∫(du)/((a^2) + (u^2))
(1/a)arctan(u/a) + C
∫(e^ku)(du)
[(1/k)(e^ku)] + C
