Differentiation Formulas
d
d
dx [f (x) ± g(x)] = f
0(x) ± g0(x) (2) d
dx [k · f (x)] = k · f
d
dx [f (x)g(x)] = f (x)g
0(x) + g(x)f0(x) (4) d
dx
f (x)
g(x)
=g(x)f
0(x) − f (x)g0(x)
d
dxf (g(x)) = f
0(g(x)) · g0(x) (6) d
dxx
d
d
d
dx tan x = sec
d
dx cot x = − csc
d
d
dx csc x = − csc x cot x (13)
d
dxe
d
dxa
d
dx ln |x| =
1
d
dx sin
−1x = √ 1
d
dx cos
−1x = −1
√
d
dx tan
−1x = 1
d
dx cot
−1x = −1
d
dx sec
−1x = 1
d
dx csc
−1x = −1
Integration Formulas
Z
Z
xndx = x
n+1
Z dx
Z
Z
axdx = 1
ln aa
Z
ln x dx = x ln x − x + C (6)
Z sin x dx = − cos x + C (7)
Z
Z tan x dx = − ln | cos x| + C (9)
Z cot x dx = ln | sin x| + C (10)
Z sec x dx = ln | sec x + tan x| + C (11)
Z csc x dx = − ln | csc x + cot x| + C (12)
Z sec2x dx = tan x + C (13)
Z csc2x dx = − cot x + C (14)
Z sec x tan x dx = sec x + C (15)
Z csc x cot x dx = − csc x + C (16)
√
a2− x2 = sin−1x
a2+ x2 =1
atan
−1x
x√
x2− a2 =1
asec
−1 |x|