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`=nax^n-1

dy=nax^n-1dx

y=auⁿ

y`=nau<sup>n-1</sup>u`

dy=nau^n-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 e^x

y`= a e^x

dy= a e^x dx

y=a e^u

y`=a u`e^u

dy= a e^u du

y=b a^x

y`=b a^x ln(a)

dy= b a^x ln(a) dx