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1 (axn)' = n·axn1 (3x2)' = 6x1

(3x9)' = 27x8

(11x3)' = 33x2

(5x9)' = 45x8

2 TRIGONOMÉTRICAS(sen(x))' = cos(x) (cos(x))' = sen(x) ( sen(f(x)) )' = cos(f(x))·f'(x) ( cos(f(x)) )' = sen(f(x))·f'(x)

( sen(6x6) )' = Cos(6x6)·( 36x5 )( Cos(6x19) )' = sen(6x19)·( 114x18 )( sen(8x21) )' = Cos(8x21)·( 168x20 )( Cos(3x19) )' = sen(3x19)·( 57x18 )( sen(4x2) )' = Cos(4x2)·( 8x1 )( Cos(2x7) )' = sen(2x7)·( 14x6 )( sen(11x16) )' = Cos(11x16)·( 176x15 )( Cos(2x17) )' = sen(2x17)·( 34x16 )

3 (f(x)n)' = nf(x)n1·f'(x) (sen9(x))' = 9·sen8(x)·cos(x)(cos14(x))' = 14·cos13(x)·sen(x)(sen15(x))' = 15·sen14(x)·cos(x)(cos14(x))' = 14·cos13(x)·sen(x)(sen4(x))' = 4·sen3(x)·cos(x)(cos9(x))' = 9·cos8(x)·sen(x)(sen10(x))' = 10·sen9(x)·cos(x)(cos3(x))' = 3·cos2(x)·sen(x)(sen4(x))' = 4·sen3(x)·cos(x)(cos18(x))' = 18·cos17(x)·sen(x)

4 (f·g)'=f '·g + f·g'(18x19·sen(x))' = 342x18·sen(x) + 18x19·cos(x)(3x11·cos(x))' = 33x10·cos(x) 3x11·sen(x)(8·sen(x))' = 0·sen(x) + 8cos(x) = 8cos(x)(16·cos(x))' = 0·cos(x) 16sen(x) = 16sen(x)

5 (fog)'(x)=(f(g(x))' = f'(g(x))·g'(x)(sen(5x6))' = (cos(5x6)) · 30x5

(6sen(1x15))' = 6cos(1x15) · 15x14

6 (f/g)' = (f '·gfg')/g2(tan(x))' = (sen(x)/cos(x))' = (cos(x)·cos(x)sen(x)·(sen(x))



)/cos2(x) = 1/cos2(x)( (17x+13)/(7x+16))' = ( (17·(7x+16) (17x+13)·7 ) / (7x+16)2

( (8x+2)/(8x+8))' = ( (8·(8x+8) (8x+2)·8 ) / (8x+8)2

( (15x+14)/(18x+15))' = ( (15·(18x+15) (15x+14)·18 ) / (18x+15)2

( (6x+2)/sen(x) )' = ( (6·sen(x) (6x+2)·cos(x) ) / sen2(x) ( (8x+7)/cos(x) )' = ( (8·cos(x) + (8x+7)·sen(x) ) / cos2(x)

7 EXPONENCIALES(ex)'=ex

(ef(x))'=ef(x)·f'(x)

(e10x8)' = (e10x

8)·(80x7)

(e8x10)' = (e8x

10)·(80x9)

(e10x7)' = (e10x

7)·(70x6)

(e4x3)' = (e4x

3)·(12x2)

(e12x7)' = (e12x

7)·(84x6)

(esen(x))' = (esen(x))·cos(x)(esen(8x))' = (esen(8x))·cos(8x)·8(esen(1x

2))' = (esen(1x2))·cos(1x2)·2x

(1f(x))' = (1f(x))·f'(x)·ln(1)(16x+11))' = (16x+11))·6·ln(1)(87x

5)' = (87x

5)·(35x4)·ln(8)

(43x+8))' = (43x+8))·3·ln(4)(43x

9)' = (43x

9)·(27x8)·ln(4)

(611x+10))' = (611x+10))·11·ln(6)(611x

7)' = (611x

7)·(77x6)·ln(6)

(34x+4))' = (34x+4))·4·ln(3)(124x

5)' = (124x

5)·(20x4)·ln(12)

(44x+5))' = (44x+5))·4·ln(4)(114x

4)' = (114x

4)·(16x3)·ln(11)

(83x+4))' = (83x+4))·3·ln(8)(113x

11)' = (113x

11)·(33x10)·ln(11)

(89x+5))' = (89x+5))·9·ln(8)

8 LOGARÍTMICAS

(ln(x))'=1/x(ln(f(x)))'= f'(x) / f(x)(loga(f(x)))'= f'(x) / f(x) · loga(e)

(ln(14x11))' = ( 154x10 ) / ( 14x11 ) (log11(15x5))' = ( 75x4 ) / ( 15x5 ) · log11(e) (ln(3x1))' = ( 3x0 ) / ( 3x1 ) (log11(6x2))' = ( 12x1 ) / ( 6x2 ) · log11(e) (ln(12x8))' = ( 96x7 ) / ( 12x8 ) (log2(18x7))' = ( 126x6 ) / ( 18x7 ) · log2(e) (ln(13x4))' = ( 52x3 ) / ( 13x4 ) (log11(12x10))' = ( 120x9 ) / ( 12x10 ) · log11(e) (ln(11x5))' = ( 55x4 ) / ( 11x5 ) (log3(11x6))' = ( 66x5 ) / ( 11x6 ) · log3(e) y' = ( x12x+13 )'= y' = y · ( (12x+13)·ln(x) )' = y · ( 12·ln(x) + (12x+13)·1/x ) =



x12x+13 · ( 12·ln(x) + (12x+13)·1/x )La expresión se puede simplificar:y' = x12x+12·( 12·ln(x) + (12x+13) )/x

y' = ( x17x+15 )'= y' = y · ( (17x+15)·ln(x) )' = y · ( 17·ln(x) + (17x+15)·1/x ) =x17x+15 · ( 17·ln(x) + (17x+15)·1/x )La expresión se puede simplificar:y' = x17x+14·( 17·ln(x) + (17x+15) )/x

y' = ( x13x+3 )'= y' = y · ( (13x+3)·ln(x) )' = y · ( 13·ln(x) + (13x+3)·1/x ) = x13x+3 ·( 13·ln(x) + (13x+3)·1/x )La expresión se puede simplificar:y' = x13x+2·( 13·ln(x) + (13x+3) )/x

y' = ( x17x+6 )'= y' = y · ( (17x+6)·ln(x) )' = y · ( 17·ln(x) + (17x+6)·1/x ) = x17x+6 ·( 17·ln(x) + (17x+6)·1/x )La expresión se puede simplificar:y' = x17x+5·( 17·ln(x) + (17x+6) )/x

y' = ( x4x+9 )'= y' = y · ( (4x+9)·ln(x) )' = y · ( 4·ln(x) + (4x+9)·1/x ) = x4x+9 · (4·ln(x) + (4x+9)·1/x )La expresión se puede simplificar:y' = x4x+8·( 4·ln(x) + (4x+9) )/x

y' = ( x14x+10 )'= y' = y · ( (14x+10)·ln(x) )' = y · ( 14·ln(x) + (14x+10)·1/x ) =x14x+10 · ( 14·ln(x) + (14x+10)·1/x )La expresión se puede simplificar:y' = x14x+9·( 14·ln(x) + (14x+10) )/x

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