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Basic differentiation and integration formulas

# Basic differentiation and integration formulas -...

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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
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