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