y=5−x2

y '=−2 x

y=4 x3+2x2+7 x+1

y '=12 x2+4 x+7

y= (x+2 )−5

y '=−5 ( x+2 )−6

y= (3 x+1 )23

y '=23

(3 x+1 )−13 (3 )

y=( x2−3x+2 )14

y '=14

(x2−3 x+2 )−34 (2x−3 )

y= x+1(2 x+3 )2

y '=(2x+3 )2 (1 )−( x+1 ) (2 ) (2 x+3 )

(2 x+3 )4

y= x2−1(x3+2 )3

y '=(x3+2 )3 (2 x )−(x2−1 ) (3 ) (x3+2 )2 (3x2 )

( x3+2 )6

y= 1−x2

(2 x+1 )4

y '=(2x+1 )4 (−2 x )−(1−x2 ) (4 ) (2x+1 )3 (2 )

(2x+1 )8

y=x 4 (7 x+1 )3

y '=x4 (3 ) (7 x+1 )2 (7 )+(7 x+1 )3 (4 x3 )

y=x 4−(7 x+1 )3

y '=4 x3−(3 ) (7 x+1 )2 (7 )

y=x3−2x2+3 x23

y '=3 x2−4 x+2 x−13

DE LA 30 EN ADELANTE

y=ln (x3+1 )2

y '=2 ( x3+1 ) (3 x2 )

(x3+1 )2

y=ln [ x3

x4+1 ]

y '=

(x 4+1 ) (3x2 )−x3(4 x3)(x4+1 )2

x3

x4+1

y=ln [ x2

x3+1 ]2

=ln [ x4

(x3+1 )2 ]

y '=

(x3+1 )2 (4 x3 )−x4(2)(x3+1)(3 x2)(x3+1 )4

x4

( x3+1 )2

y=ln [ 1−x2x3+1 ]

y '=

(x3+1 ) (−2 x )−(1−x2)(3 x2)

(x3+1 )2

1−x2

x3+1

y=ln [ x4 (x+1 )2 ]

y '=x4 (2 ) ( x+1 ) (1 )+ ( x+1 )2(4 x3)

x4 ( x+1 )2

y=ln [ (x2+1 ) (3 x+8 )−4 ]

y '=(x2+1 ) (−4 ) (3 x+8 )−5 (3 )+(3 x+8 )−4(2x )

(x2+1 ) (3 x+8 )−4

y=ln [ x3 (7 x+9 )5 ]

y '=x3 (5 ) (7 x+9 )4 (7 )+ (7 x+9 )5 (3 x2 )

x3 (7 x+9 )5

y=ln [ x4 (6x−1 )7 ]

y '=x4 (7 ) (6 x−1 )6 (6 )+(6 x−1 )7(4 x3)

x4 (6 x−1 )7

y=ln(10 x2)(x6+1)

y'=ln (10 x2 ) (6 x5 )+(x6+1)( 20 x10 x2 )

y=ln [ x4+1(11 x+20 )7 ]

y '=

(11 x+20 )7 (4 x3 )+(x¿¿4+1)(7 ) (11 x+20 )6(11)(11 x+20 )14

x4+1(11 x+20 )7

¿

y=ln (e2x+ x )

y '=e2x (2 )+1e2x+x

y=ln (e2x+16 x )

y '=e2x (2 )+16e2 x+16 x

y=sen (3 x )

y=cos (3 x ) (3 )

y=sen (x2 )

y '=cos (x2)(2 x)

y=sen (1−x2 )

y '=cos (1−x2)(−2 x)

y=sen (x2+2 x+1)

y '=cos (x2+2 x+1)(2 x+2)

y=sen ( 1x )y '=cos( 1x )( x (0 )−1(1)

x2 )

y=sen ( π3 x )y=cos( π3 x )( π3 )

y=cos (3 x )

y '=−sen (3 x ) (3 )

y=cos (ex )

y '=−sen (ex ) (e x)

y=cos (x2 )

y '=−sen (x2 ) (2x )

y=cos (lnx )

y '=−sen(lnx)( 1x )

y=cos( x

x2+1 )

y '=−sen( x

x2+1 )[ ( x2+1 ) (1 )−x (2 x)

(x2+1 )2 ]y=cos (x3+1 )

y '=−sen (x3+1 ) (3 x2 )

y=tan (7 x )

y '=Sec2 (7 x ) (7 )

y=tan (x2 )

y '=Sec2( x2)(2 x)

y=tan (x2+10x )

y '=Sec2( x2+10 x)(2x+10)

y= (sen5 x )3

y '=3 ( sen5x )2(cos 5x )(5)

y= (cos9 x )−4

y '=−4 (cos9 x )−5(−sen9 x )(9)

y= (cos2x )12

y '=12

(cos2 x )−12 (−sen2 x ) (2 )

y=Sec 8x

y '=Sec8 xTan 8x (8 )

y=Sec10 x

y '=Sec10 xTan10 x (10 )

y=Sec (x2+5 )

y '=Sec (x2+5 ) tan(x2+5)(2 x)

y=Sec (6 x+1 )

y '=Sec (6 x+1 ) tan(6 x+1)(6)

y=Csc (x2+2 )

y '=−Csc (x2+2)cot(x2+2)(2 x)

y=Csc (e3x )

y '=−Csc (e3 x )cot (e3 x ) (e3 x ) (3 )

y=Csc (x2+1 )

y '=−Csc ( x2+1 )cot (x2+1 ) (2x )

y=cot (x+1 )

y '=−Csc2(x+1)(1)

y=cot (4 x )

y '=−Csc2(4 x )(4 )

y=cot (x+1 )

y '=−Csc2(x+1)(1)

y=cot (5x )

y '=−Csc2(5 x)(5)