![Differentiation Formulas
d
dx
k = 0 (1)
d
dx
[f(x) ± g(x)] = f (x) ± g (x) (2)
d
dx
[k · f(x)] = k · f (x) (3)
d
dx
[f(x)g(x)] = f(x)g (x) + g(x)f (x) (4)
d
dx
f(x)
g(x)
=
g(x)f (x) − f(x)g (x)
[g(x)]
2 (5)
d
dx
f(g(x)) = f (g(x)) · g (x) (6)
d
dx
xn
= nxn−1
(7)
d
dx
sin x = cos x (8)
d
dx
cos x = − sin x (9)
d
dx
tan x = sec2
x (10)
d
dx
cot x = − csc2
x (11)
d
dx
sec x = sec x tan x (12)
d
dx
csc x = − csc x cot x (13)
d
dx
ex
= ex
(14)
d
dx
ax
= ax
ln a (15)
d
dx
ln |x| =
1
x
(16)
d
dx
sin−1
x =
1
√
1 − x2
(17)
d
dx
cos−1
x =
−1
√
1 − x2
(18)
d
dx
tan−1
x =
1
x2 + 1
(19)
d
dx
cot−1
x =
−1
x2 + 1
(20)
d
dx
sec−1
x =
1
|x|
√
x2 − 1
(21)
d
dx
csc−1
x =
−1
|x|
√
x2 − 1
(22)
Integration Formulas
dx = x + C (1)
xn
dx =
xn+1
n + 1
+ C (2)
dx
x
= ln |x| + C (3)
ex
dx = ex
+ C (4)
ax
dx =
1
ln a
ax
+ C (5)
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
√
a2 − x2
= sin−1 x
a
+ C (17)
dx
a2 + x2
=
1
a
tan−1 x
a
+ C (18)
dx
x
√
x2 − a2
=
1
a
sec−1 |x|
a
+ C (19)](https://image.slidesharecdn.com/c02-150511103559-lva1-app6892/85/maths-basics-1-320.jpg)
maths basics
- 1. Differentiation Formulas d dx k = 0 (1) d dx [f(x) ± g(x)] = f (x) ± g (x) (2) d dx [k · f(x)] = k · f (x) (3) d dx [f(x)g(x)] = f(x)g (x) + g(x)f (x) (4) d dx f(x) g(x) = g(x)f (x) − f(x)g (x) [g(x)] 2 (5) d dx f(g(x)) = f (g(x)) · g (x) (6) d dx xn = nxn−1 (7) d dx sin x = cos x (8) d dx cos x = − sin x (9) d dx tan x = sec2 x (10) d dx cot x = − csc2 x (11) d dx sec x = sec x tan x (12) d dx csc x = − csc x cot x (13) d dx ex = ex (14) d dx ax = ax ln a (15) d dx ln |x| = 1 x (16) d dx sin−1 x = 1 √ 1 − x2 (17) d dx cos−1 x = −1 √ 1 − x2 (18) d dx tan−1 x = 1 x2 + 1 (19) d dx cot−1 x = −1 x2 + 1 (20) d dx sec−1 x = 1 |x| √ x2 − 1 (21) d dx csc−1 x = −1 |x| √ x2 − 1 (22) Integration Formulas dx = x + C (1) xn dx = xn+1 n + 1 + C (2) dx x = ln |x| + C (3) ex dx = ex + C (4) ax dx = 1 ln a ax + C (5) 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 √ a2 − x2 = sin−1 x a + C (17) dx a2 + x2 = 1 a tan−1 x a + C (18) dx x √ x2 − a2 = 1 a sec−1 |x| a + C (19)