matematikk.net

Funksjonen w(x,y,z) er gitt ved

w(x,y,z) = x/z + y/z , der x = cost*cost , y = sint*sint og z = 1/t^2

finn [symbol:diff] w / [symbol:diff] x

altså partiell derivert

t^2

Forrige svar er jo riktig, men her er en forklaring.
Du partiellderiverer på vanlig måte mhp x og oppnår

[tex]\frac{\partial w}{\partial x}=\frac{1}{z}\cdot 1[/tex]

Så gjenstår å sette inn [tex]z=\frac{1}{t^2}[/tex]

Vi oppnår [tex]\frac{\partial w}{\partial x}=\frac{1}{\frac{1}{t^2}}=t^2[/tex]

A constant function and e^x are walking on Broadway. Then suddenly the constant function sees a differential operator approaching and runs away. so e to-the x follows him and asks why the hurry.

"Well, you see, there's this diff.operator coming this way, and when we meet, he'll differentiate me and nothing will be left of me...!"

"Ah," says e^x, "he won't bother ME, I'm e to-the x!" and he walks on. Of course he meets the differential operator after a short distance.

e^x : "Hi, I'm e^x"

diff.op. : "Hi, I'm d/dy"