Reglas De Derivacion

EJERCICIOS

I. ddx C = 0 ddx 25 = 0

II. ddx xn = nxn-1 ddx 12x3 = 36x2

III. ddx (u+v) = ddx u + ddx v ddx (5x2+7x+2) = ddx 5x2 + ddx 7x +ddx 2 = 10x + 7

IV. ddx (u-v) = ddx u - ddx v ddx (8x3-27x) = ddx 8x3 - ddx 27x = 24x2 – 27

V. ddx (Cu) = C ddx u ddx 7x4 = 7 ddx x4 = 7 ( 4x3) = 28 x3

VI. ddx (uv) = u ddx v + v ddx u ddx ( cosx * sen2x ) = (cosx)( ddx sen2x) + (sen2x)(ddx cosx) = cosx * 2cos2x + sen2x * -senx = 2cos2x * cosx – sen2x * senx

VII. ddx ( uv ) = V ddx u - u ddx vv2 ddx ( 1senx + x3 ) = (senx + x3)( ddx 1) - (1)( ddx senx + ddx x3 )(senx + x3)2 = (senx + x3)(0) - (1)(cosx + 3x2)(senx + x3)2 = -cosx - 3x2(senx + x3)2

VIII. ddx senv = cosv * ddx v ddx senx4 = cosx4 * ddx x4 = 4x3 cosx4

IX. ddx cosv = -senv * ddx v ddx cos(3x2+x-1) = [-sen(3x2+x-1)] [ddx 3x2 + ddx x - ddx 1] = [6x +1][-sen(3x2+x-1)]

X. ddx tanv = sec2v * ddx v ddx tan2x = 2 tanx sec2x

XI. ddx cotv = -csc2v * ddx v ddx cot 4x2 = (-csc2 4x2)(8x) = -8x csc2 4x2

XII. ddx secv = secv tanv ddx v ddx sec 5x = 5 sec 5x tan 5x

XIII. ddx cscv = -cscv cotv ddx v ddx csc(x2 ) = - 12 csc( x2 ) cot( x2 )

XIV. ddx ev = ev ddx v ddx e2x = 2e2x

XV. ddx Ln v = 1v ddx v ddx Ln(6x5) = ( 16x5 )(30x4) = 5x

XVI. ddx (fºg)(x) = f ’(g(x)) * g‘(x) ddx (5x3)4 =4(15x2)(5x3)3 = 60x2(5x3)3

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