class xii -differntiation & integration formulae.
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 x n = nx n-1 (7) d dx sin x = cos x (8) d dx cos x = - sin x (9) d dx tan x = sec 2 x (10) d dx cot x = - csc 2 x (11) d dx sec x = sec x tan x (12) d dx csc x = - csc x cot x (13) d dx e x = e x (14) d dx a x = a x ln a (15) d dx ln |x| = 1 x (16) d dx sin -1 x = 1 √ 1 - x 2 (17) d dx cos -1 x = -1 √ 1 - x 2 (18) d dx tan -1 x = 1 x 2 +1 (19) d dx cot -1 x = -1 x 2 +1 (20) d dx sec -1 x = 1 |x| √ x 2 - 1 (21) d dx csc -1 x = -1 |x| √ x 2 - 1 (22) Integration Formulas dx = x + C (1) x n dx = x n+1 n +1 + C (2) dx x = ln |x| + C (3) e x dx = e x + C (4) a x dx = 1 ln a a x + 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) sec 2 x dx = tan x + C (13) csc 2 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 √ a 2 - x 2 = sin -1 x a + C (17) dx a 2 + x 2 = 1 a tan -1 x a + C (18) dx x √ x 2 - a 2 = 1 a sec -1 |x| a + C (19)
-
Upload
mandeep-singh-plaha -
Category
Documents
-
view
2.035 -
download
4
description
formulaes..
Transcript of class xii -differntiation & integration formulae.
Differentiation Formulas
d
dxk = 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
dxf(g(x)) = f ′(g(x)) · g′(x) (6)
d
dxxn = nxn−1 (7)
d
dxsinx = cos x (8)
d
dxcos x = − sinx (9)
d
dxtanx = sec2 x (10)
d
dxcot x = − csc2 x (11)
d
dxsec x = sec x tanx (12)
d
dxcsc x = − csc x cot x (13)
d
dxex = ex (14)
d
dxax = ax ln a (15)
d
dxln |x| = 1
x(16)
d
dxsin−1 x =
1√1− x2
(17)
d
dxcos−1 x =
−1√1− x2
(18)
d
dxtan−1 x =
1x2 + 1
(19)
d
dxcot−1 x =
−1x2 + 1
(20)
d
dxsec−1 x =
1|x|√
x2 − 1(21)
d
dxcsc−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 =
1ln a
ax + C (5)
∫lnx dx = x lnx− x + C (6)
∫sinx dx = − cos x + C (7)
∫cos x dx = sinx + C (8)
∫tanx dx = − ln | cos x|+ C (9)
∫cot x dx = ln | sinx|+ C (10)
∫sec x dx = ln | sec x + tanx|+ 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 tanx 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=
1a
tan−1 x
a+ C (18)
∫dx
x√
x2 − a2=
1a
sec−1 |x|a
+ C (19)
