- #1

- 14

- 0

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Phyman1109
- Start date

- #1

- 14

- 0

- #2

mathman

Science Advisor

- 7,924

- 467

df/dt = (∂f/∂u)du/dt + (∂f/∂v)dv/dt + (∂f/∂w)dw/dt.

- #3

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 963

(This is NOT the question mathman answered. He appears to be thinking you were asking about the derivative being 0, not "f(u,v,w)=0".

As long as F(x, y, z) has continuous partial derivtives, and x, y, and z are differentiable functions of t,

[tex]\frac{dF}{dt}= \frac{\partial F}{\partial x}\frac{dx}{dt}+ \frac{\partial F}{\partial y}\frac{dy}{dt}+ \frac{\partial F}{\partial z}\frac{dz}{dt}[/tex]

so that if all partial derivatives of F, with respect to x, y, and z, the dF/dt= 0 for any parameter, t. But if dF/dt= 0 for some t, it does NOT follow that the partial derivatives are 0.)

- #4

Office_Shredder

Staff Emeritus

Science Advisor

Gold Member

- 4,326

- 434

Share: