Differentiation Formulas Math

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