Tabla de Derivadas
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TABLA DERIVADAS 1 2 3 4 5 6 7 8 9 10 11 12 Por: Fernando Valdés M ©, UTP, Pereira d (cu) = cu′ dx d (uvw) = u′ vw + uv ′ w + uvw′ dx d n (u ) = nun−1 u′ dx d (u + v) = u′ + v ′ dx d ( u ) vu′ − uv ′ = dx v v2 d u ′ |u| = u dx |u| d (uv) = u′ v + uv ′ dx d (c) = 0 dx d 1 ln(u) = u′ dx u d u (e ) = eu u′ dx d cos(u) = − sen(u) u′ dx d sec(u) = sec(u) tan(u) u′ dx d f (g(x)) = f ′ (g(x))g ′ (x) dx d sen(u) = cos(u) u′ dx d cos(ku) = − sen(ku)ku′ dx d cot(u) = − csc2 (u) u′ dx 1 d loga (u) = u′ dx u ln(a) d sen(ku) = cos(ku) ku′ dx d tan(u) = sec2 (u) u′ dx d csc(u) = − csc(u) cot(u) u′ dx d u a = au ln(a) u′ dx 1 d arc sen(u) = √ u′ dx 1 − u2 d senh(u) = cosh(u) u′ dx d sech(u) = −sech(u) tanh(u) u′ dx d 1 u′ senh−1 (u) = √ dx 1 + u2 d 1 u′ sech−1 (u) = − √ dx u 1 − u2 1 d arc cos(u) = − √ u′ dx 1 − u2 1 d arctan(u) = u′ dx 1 + u2 d cosh(u) = senh(u) u′ dx d csch(u) = −csch(u) coth(u) u′ dx d 1 u′ cosh−1 (u) = √ dx u2 − 1 d 1 u′ csch−1 (u) = − √ dx |u| 1 + u2 d tanh(u) = sech2 (u) u′ dx d coth(u) = −csch2 (u) u′ dx d 1 tanh−1 (u) = u′ dx 1 − u2 d 1 coth−1 (u) = u′ dx 1 − u2 TRIGONOMETRÍA HIPERBÓLICA 3 ex + e−x 2 cosh2 (x) − senh2 (x) = 1 √ senh−1 (x) = ln(x + x2 + 1) 4 senh2 (x) = 1 2 cosh(x) = −1 + cosh(2x) 2 ex − e−x 2 1 − tanh2 (x) = sech2 (x) √ cosh−1 (x) = ln(x + x2 − 1) senh(x) = cosh2 (x) = 1 + cosh(2x) 2 1 senh(x) cosh(x) coth2 (x) − 1 = csch2 (x) ( ) 1 1+x tanh−1 (x) = ln 2 1−x tanh(x) = cosh(2x) = cosh2 (x) + senh2 (x)
