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27. y=1+sen2x1+cos2x

y'=1+sen2x1+cos2x

y'=1+sen2x'1+cos2x-1+sen2x1+cos2x'(1+cos2x)2

y'=(1)+(sen2x)''1+cos2x-1+sen2x(1)+(cos2x)'(1+cos2x)2

y'=2senx(senx)'1+cos2x-1+sen2x(2)(cosx)(cosx)'(1+cos2x)2

y'=2senxcos x(x)'1+cos2x-1+sen2x(2)(cosx)(-senx)(x)'(1+cos2x)2

y'=2senx. cosx1+cos2x-1+sen2x2cosx.senx(1+cos2x)2

y'=2senx. cosx1+cos2x+1+sen2x(1+cos2x)2

y'=2senx. cosx1+1+1(1+cos2x)2

y'=2senx. cosx3(1+cos2x)2

y'=6senxcosx(1+cos2x)2

28. y=x2ex3

y'=x21ex3+x2ex31

y'=2xx'ex3+x2ex3(x3)’

y'=2x.ex3+x2.ex33x2(x)'y'=2x.ex3+x2.ex3.3x2

y'=ex3x(2+3x3)

29. y=ex2+1

(y)'=ex2+1'

y'=ex2+1x2+11

y'=ex2+112x2+1(x2+1)1

y'=ex2+12x2+1x21+(1)1

y'=ex2+12x2+12xx1+0

y'=ex2+12x2+12x

y'=x.ex2+1x2+1

30. y=x2+x+1x3-65

y'=x2+x+1x3-651
y'=5x2+x+1x3-64x2+x+1x3-61

y'=5x2+x+1x3-64x2+x+1x3-6-x2+x+1x3-61x3-62

y'=5x2+x+1x3-64x21+x1+(1)1x3-6-x2+x+1x31-61x3-62

y'=5x2+x+1x3-642xx1+1+0x3-6-x2+x+13x2(x1-0x3-62y'=5x2+x+1x3-642x+1x3-6-x2+x+13x2x3-62

y'=5x2+x+1x3-642x4+12x+x-6- 3x4+3x3+3x2x3-62

y'=5x2+x+1x3-642x4+12x+x-6-3x4+3x3+3x2 x3-62

y'=5x2+x+1x3-64-x4-2x3-3x2-12x-6 x3-62

31. y=senx+cosxsenx-cosx3

Iny = lnsenx+cosxsenx-cosx3

Lny = 3lnsenx+cosxsenx-cosx

Lny = 3 (ln(senx+cosx)-ln (senx-cosx))

(Lny)’ = 3 (ln(senx+cosx)-ln (senx-cosx))’

y'y=3(lnsenx+cosx-ln senx-cosx)'y'y=3senx+cosx'senx+cosx-senx-cosx'senx-cosx

y'y=3senx)'+(cosx'senx+cosx-senx)'-(cosx'senx-cosx

y'y=3cosxx'+(-senx)(x)'senx+cosx-cosxx'-(-senx)(x)'senx-cosx

y'y=3cosx-senxsenx+cosx-cosx+senxsenx-cosx

y'y=3cosx-senxsenx-cosx-cosx+senxsenx+cosxsenx+cosxsenx-cosx

y'y=3cosx-senx-cos2x-sen2x+senxcosx-cosx-senx-cos2x-sen2x+senxcosx senx+cosxsenx-cosx

y'y=32senx.cosx-1- 2senx.cosx+1senx+cosxsenx-cosx

y'y=32senx.cosx-1- 2senx.cosx-1 senx+cosxsenx-cosx

y'y=3-2 senx+cosxsenx-cosx

y'=-6senx+cosxsenx-cosxsenx+cosx3senx+cosx3

y'=-6senx+cosx2senx+cosx4

y'=-6senx+cosx2senx-cosx2senx-cosx(senx-cosx)

y'=-6senx+cosx2senx-cosx2sen2.senx.cosx-senx.cosx+cosx

y'=-61-2senx.cosxsenx+cosx2senx-cosx2

32. y=x.e1/x2

y=x.ex-2

y'=x.ex-2'

y'=x'ex-2+xex-2'y'=ex-2+xex-2x-2'

y'=ex-2+xex-2-2x-3(x)'

y'=ex-2+xex-2-2x-3

y'=ex-21+2x2

33. y=secx2+cosecx2

y'=secx2+cosecx2

y'=secx2'+(cossec(x2))'

y'=secx2 .tgx2(x2)'+-cosecx2(cotg(x2)(x2)'

y'=secx2 .tgx2(2x)(x)'+-cosex2(cotg(x2)(2x)(x)'

y'=2x(secx2.tgx2-cosecx2cot x2)

34. y=1-cos(x2)1+cos(x2)

lny=ln1-cosx21+cosx2

lny=ln1-cosx2-ln⁡(1+cosx2)

lny'=ln1-cosx2-ln⁡(1+cosx2)’y'y=ln1-cosx2'-ln⁡(1+cosx2)'

y'y=(1-cosx2)'1-cosx2-(1+cosx2)'1+cosx2-

y'y=1'-(cosx2)'1-cosx2-1'+(cosx2)'1+cosx2-

y'y=0--senx2(x2)'1-cosx2-0+-senx2(x2)'1+cosx2-

y'y=senx2.2x(x)'1-cosx2--senx2.(2x)(x)'1+cosx2-

y'y=2x.senx21-cosx2+senx2.2x1+cosx2-

y'y=2x.senx211-cosx2+11+cosx2-

y'y=2x.senx21+cosx2+1-cosx21-cosx21+cosx2

y'y=2x.senx221-cosx21+cosx2

y'y=4x.senx21-cosx21+cosx2y'=4x.senx21-cosx21+cosx21-cosx21+cosx2

y'=4x.sen(x2)1-cos(x2)2

35. y=(1+esenx)3

lny=ln⁡(1+esenx)3

lny=3ln⁡(1+esenx)'

lny'=3(ln⁡(1+esenx))'

y'y=31+esenx11+esenx

y'y=31'+(esenx)'1+esenx

y'y=3(0+esenxsen')1+esenx

y'y=3esenx.cos.(x)'1+esenx

y'y=3cosxesenx1+esenx(1+esenx)3

y'y=3cosxesenx.(1+esenx)3

36. y=ln1+ex-1-ln(1+ex+1)

(y)'=ln1+ex-1'-ln(1+ex+1)'y'=1+ex-111+ex-1-1+ex+111+ex+1

y'=(1+ex)'21+ex-01+ex-1-(1+ex)'21+ex+01+ex+1

y'=1'+(ex)'21+ex1+ex-1-0'+ex'(x)21+ex1+ex+1

y'=ex21+ex*11+ex-1- ex21+ex*11+ex+1

y'=ex21+ex 11+ex-1- 11+ex+1

y'=ex21+ex 1+ex+1-1+ex+11+ex-1

y'=ex21+ex 2ex

y'=11+ex

37. y=lnxx2+9

y=lnx-lnx2+9

y=lnx-12ln⁡(x2+9)

y'=lnx1-12ln⁡(x2+9)1

y'=1xx1-12ln⁡(x2+9)1

y'=1x-12(x2+9)'x2+9

y'=1x-12x2+(9)'x2+9...