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1º Bachillerato CNS Derivadas - 1

1 Bachillerato CNSD erivadas - 1 EJERCICIOS DE Derivadas FUNCI N y=3y =0 y=x+5y =1 y=x7y'= y=x6 x3y'=6x5 y=2x4y'= y=ax by'= y=5x 2y'= y=a5y'= y=ax2 bx cy'=2ax y=x x 1 y'=2x y= x 1 x 1 y'= y=ax3 bx2 cx dy'=3ax2 2bx y=x3 x2 4x 5y'=3x2 2x y=x4 4x3 5x2y'=4x3 12x2 y=2x3 3x2 6x 5y'=6x2 6x y= x 1 x2 x 3 y'=3x2 y=x x 1 2y'=3x2 4x y=a x 1 2y'=2a x 1 y=a a 1 2y'= y=x 2y'= y=1x 1y'= 1 x 1 y=x2 3x3 xy'= x4 10x2 3 x3 x y=x 1xy'= y=x x 1 x 1 3x2 3y'=3x4 6x2 3 3x2 3 y=x x 2 2x2 4x 4y'= y= 3x 2y'=32 3x 2 Derivadas - y= 2x 1y'=1 2x y= x2 1y'=x x2 y= 1 x1 xy'= 1 1 x 2 1 x1 y=1 x 1 x2y'=1 1 x 1 y=e4xy'= y=52xy'=2 52x y=e3 x2y'= 2xe3 y=ex e x2y'=ex e y=x3 2x exy'=x2 2x ex 3 xln2 x y=ex e

1º Bachillerato CNS Derivadas - 1 EJERCICIOS DE DERIVADAS FUNCIÓN DERIVADA

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Transcription of 1º Bachillerato CNS Derivadas - 1

1 1 Bachillerato CNSD erivadas - 1 EJERCICIOS DE Derivadas FUNCI N y=3y =0 y=x+5y =1 y=x7y'= y=x6 x3y'=6x5 y=2x4y'= y=ax by'= y=5x 2y'= y=a5y'= y=ax2 bx cy'=2ax y=x x 1 y'=2x y= x 1 x 1 y'= y=ax3 bx2 cx dy'=3ax2 2bx y=x3 x2 4x 5y'=3x2 2x y=x4 4x3 5x2y'=4x3 12x2 y=2x3 3x2 6x 5y'=6x2 6x y= x 1 x2 x 3 y'=3x2 y=x x 1 2y'=3x2 4x y=a x 1 2y'=2a x 1 y=a a 1 2y'= y=x 2y'= y=1x 1y'= 1 x 1 y=x2 3x3 xy'= x4 10x2 3 x3 x y=x 1xy'= y=x x 1 x 1 3x2 3y'=3x4 6x2 3 3x2 3 y=x x 2 2x2 4x 4y'= y= 3x 2y'=32 3x 2 Derivadas - y= 2x 1y'=1 2x y= x2 1y'=x x2 y= 1 x1 xy'= 1 1 x 2 1 x1 y=1 x 1 x2y'=1 1 x 1 y=e4xy'= y=52xy'=2 52x y=e3 x2y'= 2xe3 y=ex e x2y'=ex e y=x3 2x exy'=x2 2x ex 3 xln2 x y=ex e xex e xy'=4 ex e x y=ax2 x 1y'= 2x 1 ax2 x 1 y=ln x2 1 y'=2xx2 y=ln ax2 bx c y'=2ax bax2 bx y=ln53xy'= y=x5lnxy'=x4 5lnx 1 y=x2ln 2 x y'=x 2ln 2 x x2 x y=lnxxy'=1 y=lg3 1 x2 y'=2x1 y=ln x 5 y'=1x y=lga 3x2 5 y'=6x3x2 y=x lnx xy'= y=ln 1 x2y'=x1 x21

2 Bachillerato CNSD erivadas - y=ln 1 x1 xy'= 11 y=lnx2 1x2 1y'= 4xx4 y=sen2xy'= y=cos 2x 1 y'= 2sen 2x 1 y=tg x2 x 1 y'= 2x 1 sec2 x2 x 1 y=tg xy'=12 xsec2 y=sec 3x2 4x 1 y'= 6x 4 sec 3x2 4x 1 tg 3x2 4x 1 y=cosecxay'= y= sen3xy'=3cos3x2 y=sen2/3xy'=23sen 1/3x cosx=2cosx33 y=xcosxy'=cosx y=lnsenxy'= y=senx cos2xy'=cosx cos2x 2senx y=extgxy'=ex tgx sec2x =ex tg2x tgx 1 y=arcsen2xy'=2 1 y=arcsen xy'=12 1 x x=12 x y=arccos x2 1 y'= 2x 1 x2 1 y=13tg3x tgx+xy'=tg2x sec2x sec2x y=arctg1 x1 xy'=11 y= 1 senx1 senx 2y'= 4 1 senx cosx 1 senx y=lntgxy'= y=ln 1 cosx1 cosxy'= y=ln senxy'=ctg2xDerivadas - y=arcsecx2y'=2x x4 y=arcctg 2x 1 y'= 2 2x 1 2 y=sen sen2x y'=2cos2x cos sen2x y=sen ln 3x 5 y'=33x 5cos ln 3x 5 y=arcsen cosx x y'= senx 1 1 cosx x y=ln x lnx y'=x 1x2 y=arcsen 11 x2 y'= 2 1 x2 x2 y=lg lgxx y'=loge y=ln1/2sen2xy'=ctg2x y=x2cos3xy'=2xcos3x y=xx 1y'=[lnx x 1x]xx y= 1 1x xy'=[lnx 1x 1x 1] 1 1x y= x5 x2 1 y'=[10xlnx 5x2 5x] x5 x2 y=xexy'=[exlnx exx] y= 3x 1 2x 3y'=[2ln 3x 1 6x 93x 1] 3x 1 2x y= senx xy'=[ln senx xctgx]

3 Senx y=xsen 2x 9 y'=[2cos 2x 9 lnx sen 2x 9 x]xsen 2x 9 y= senx cosxy'=[ senxln senx cosxctgx] senx y= lnx lnxy'=1x[ln lnx 1] lnx y= x2 1 senxy'=[cosxln x2 1 2xsenxx2 1] x2 1 senx1 Bachillerato CNSD erivadas - 5 REGLAS DE DERIVACI NA. Suma y v y'=u' v'y=u v y'=u' v'B. Producto y v y'=u' v u v'y=uv y'=u' v u v'v2C. Producto por un n y=a u y'=a u'D. Composici ny=[g f x ]'=g' f x f' x TIPOSFORMASSIMPLESCOMPUESTAS1. Tipo Potencialy=xn y'=nxn 1y=k y'=0y= x y'=12 xy=un y'=nun 1u'y= u y'=u'2 u2. Tipo logar tmicoy=lnx y'=1xy=lgax y'=1xlgaey=lnu y'=u'uy=lgau y'=u'ulgae3.

4 Tipo exponencialy=ex y'=exy=ax y'=axlnay=eu y'=eu u'y=au y'=au u' lna4. Tipo circulary=senx y'=cosxy=cosx y'= senxy=tgx y'=1 tg2x=sec2xy=cosecx y'= cosecx ctgxy=secx y'=secx tgxy=ctgx y'= cosec2xy=senu y'=cosu u'y=cosx y'= senu u'y=tgu y'= 1 tg2u u'=sec2u u'y=cosecu y'= cosecu ctgu u'y=secu y'=secu tgu u'y=ctgu y'= cosec2u u'5. Tipo funciones arcoy=arcsenx y'=1 1 x2y=arccosx y'= 1 1 x2y=arctgx y'=11 x2y=arccosecx y'= 1x x2 1y=arcsecx y'=1x x2 1y=arcctgx y'= 11 x2y=arcsenu y'=u' 1 u2y=arccosu y'= u' 1 u2y=arctgu y'=u'1 u2y=arccosecu y'= u'u u2 1y=arcsecu y'=u'u u2 1y=arcctgu y'= u'1 u2