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d dx f x + g(x) = f′ x + g x

d dx

cf(x) = cf′(x)

d dx f x g(x) = f x g′ x + g x f′(x)

d dx f(x)/g(x) = g x f′ x −f x g′(x)

g x 2

d dx xn = nx n−1

d dx

sin (u) = cos u u′

cos u = − sin u u′

d dx tan (u) = sec2 u u′

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sin a + b = sin a cos b + cos a sin b 2 π − a 2 cos a + b = cos a cos b − sin a sin b cos = sin (a) sin 2 1−cos (2a) a = 2 cos 2 1+cos (2a) (a) = 2 sin −a = −sin (a) 45º cos −a = cos (a) tan −a = −tan (a) sin 2a = 2 sin a cos (a) cos 2a = cos 2 a − sin 2 (a) sin 2 a + cos 2 a = 1 1 + tan 2 a = sec 2 (a) 2 1 + cot 2 a = csc 2 (a) sin π − a 2 = cos (a) 60º 1 1 30º 3 1

d dx f x + g(x) = f′ x + g x d dx cf(x) = cf′(x) d dx f x g(x) = f x g′ x + g x f′(x) d dx f(x)/g(x) = g x f′ x −f x g′(x) g x 2 d dx xn = nx n−1 d dx d dx sin (u) = cos u u′ cos u = − sin u u′ d dx tan (u) = sec2 u u′

Page 1: UNIVERSITARIO INSUCO
Page 5 and 6: f x cf x + g(x) dx = f x dx + g x
Page 7 and 8: sinh u du = cosh u cosh u du = sin
Page 9: du a 2 −u 2 = sin−1 u a + c du

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