Question

formulae of differentiation and integration

Answer 1

d dx k = 0 (1) d dx [ f ( x ) ± g ( x)] = f 0 ( x ) ± g 0 ( x) (2) d dx [ k · f ( x)] = k · f 0 ( x) (3) d dx [ f ( x ) g ( x)] = f ( x ) g 0 ( x) + g ( x ) f 0 ( x) (4) d dx f ( x ) g ( x ) = g ( x ) f 0 ( x ) − f ( x ) g 0 ( x ) [ g ( x)] 2 (5) d dx f ( g ( x)) = f 0 ( g ( x)) · g 0 ( 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| = 1x (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|√x2 − 1 (22)