Differentiation Formulas Integration Formulas

[Pages:1]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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