Derivate si diferentialele catorva functii elementare

Functia

Derivata

Diferentiala

y=a*)

y`=0

dy=0

y=x

y`=1

dy=dx

y=ax

y`=1

dy=dx

y=u**)

y`=u`

dy=du

y=au

y`=au`

dy=adu

y=u+v

y`=u`+v`

dy=du+dv

y=uv

y`=u`v+uv`

dy=vdu+udv

y=axn

y`=naxn-1

dy=naxn-1dx

y=aun

y`=naun-1u`

dy=naun-1du

y=sinx

y`=cosx

dy=cosx dx

y=sinu

y`=u`cosu

dy=cosu du

y=cosx

y`=-sinx

dy=-sinx dx

y=cosu

y`=-u`sinu

dy=-sinu du

y=a ex

y`= a ex

dy= a ex dx

y=a eu

y`=a u`eu

dy= a eu du

y=b ax

y`=b ax ln(a)

dy= b ax ln(a) dx

*)         a,b – constante

**)       u,v – functii

 

 

Primitive ale catorva functii elementare

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