Differentiation Formulas Integration Formulas
Differentiation Formulas
d
k=0
(1)
dx
d
[f (x) ? g(x)] = f (x) ? g (x)
(2)
dx
d
[k ? f (x)] = k ? f (x)
(3)
dx
d [f (x)g(x)] = f (x)g (x) + g(x)f (x) (4)
dx
d f (x) g(x)f (x) - f (x)g (x)
= dx g(x)
[g(x)]2
(5)
d
f (g(x)) = f (g(x)) ? g (x)
(6)
dx
d xn = nxn-1
(7)
dx
d
sin x = cos x
(8)
dx
d
cos x = - sin x
(9)
dx
d tan x = sec2 x
(10)
dx
d cot x = - csc2 x
(11)
dx
d
sec x = sec x tan x
(12)
dx
d
csc x = - csc x cot x
(13)
dx
d ex = ex
(14)
dx
d ax = ax ln a
(15)
dx
d
1
ln |x| =
(16)
dx
x
d sin-1 x = 1
(17)
dx
1 - x2
d cos-1 x = -1
(18)
dx
1 - x2
d dx
tan-1
x
=
1 x2 +
1
(19)
d dx
cot-1
x
=
-1 x2 +
1
(20)
d sec-1 x = 1
(21)
dx
|x| x2 - 1
d csc-1 x =
-1
(22)
dx
|x| x2 - 1
Integration Formulas
dx = x + C
(1)
xn dx = xn+1 + C
(2)
n+1
dx
= ln |x| + C
(3)
x
ex dx = ex + C
(4)
ax dx = 1 ax + C
(5)
ln a
ln x dx = x ln x - x + C
(6)
sin x dx = - cos x + C
(7)
cos x dx = sin x + C
(8)
tan x dx = - ln | cos x| + C
(9)
cot x dx = ln | sin x| + C
(10)
sec x dx = ln | sec x + tan x| + C (11)
csc x dx = - ln | csc x + cot x| + C (12)
sec2 x dx = tan x + C
(13)
csc2 x dx = - cot x + C
(14)
sec x tan x dx = sec x + C
(15)
csc x cot x dx = - csc x + C
(16)
dx
= sin-1 x + C
(17)
a2 - x2
a
dx a2 + x2
=
1 a
tan-1
x a
+C
(18)
dx
= 1 sec-1 |x| + C
(19)
x x2 - a2 a
a
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