Derivasjon - flervariabel
Moderators: Vektormannen, espen180, Aleks855, Solar Plexsus, Gustav, Nebuchadnezzar, Janhaa
-
Ron Wood
Skal derivere f(x,y,z)= (x*z)/(y+z) mhp. z, altså d/dz, men får stadig feil svar, noen som kunne ta den?
-
Solar Plexsus
- Over-Guru
- Posts: 1686
- Joined: 03/10-2005 12:09
df/dz
= [xz/(y + z)]' ([g(x,y,z)]' betyr her dg/dz)
= x*[z/(y + z)]'
= x [(z)'*(y + z) - z*(y + z)'] / (y + z)[sup]2[/sup]
= x [1*(y + z) - z*1] / (y + z)[sup]2[/sup]
= xy / (y + z)[sup]2[/sup].
= [xz/(y + z)]' ([g(x,y,z)]' betyr her dg/dz)
= x*[z/(y + z)]'
= x [(z)'*(y + z) - z*(y + z)'] / (y + z)[sup]2[/sup]
= x [1*(y + z) - z*1] / (y + z)[sup]2[/sup]
= xy / (y + z)[sup]2[/sup].
-
Solar Plexsus
- Over-Guru
- Posts: 1686
- Joined: 03/10-2005 12:09
d/dy [x[sup]y*lnz[/sup]] = d/dy [(x^lnz)[sup]y[/sup]] = (x^lnz)[sup]y[/sup] * ln(x[sup]lnz[/sup]) = lnz*lnx*x[sup]y*lnz[/sup].