1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Chain rule confusion! partial derivatives

  1. Oct 19, 2005 #1
    Hello everyone...
    I'm very confused....
    i'm suppose to find
    dz/dt and dw/dt
    but for some of the questions there is no w variable! so what do u put for dw/dt?! Also i have the following:
    w = xy + yz^2; x = e^t; y = e^t*sint; z = e^t*cost;
    so i'm trying to find dz/dt and dw/dt;
    dz/dt = dz/dx * dx/dt + dz/dy * dy/dt + dz/dw * dw/dt;
    but when i try dz/dx * dx/dt i need to first take the partial derivative of z with respect to x, but as you can see, z has no x variable!! so what do i do about that? THanks!
  2. jcsd
  3. Oct 19, 2005 #2
    how do you get dz/dt = dz/dx * dx/dt +dz/dy * dy/dt + dz/dw * dw/dt

    dz/dt[e^t * cos t] = cos t * e^t - sint * e^t

    there is no dx

    as far as dw/dt

    it would be

    dw/dx * dx/dt + dw/dy * dy/dt + dw/dz + dz/dt
  4. Oct 19, 2005 #3

    James R

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member


    You need to keep track of what is a function of what.

    You have:

    [tex]w = xy + yz^2; x = e^t; y = e^t \sin t; z = e^t \cos t[/tex]

    So, you have:

    [tex]w = w(x,y,z); x = x(t); y = y(t); z=z(t)[/tex]

    If you want to find dz/dt, it's just a simple derivative, since z is only a function of t, and not of x or y or w.

    To find dw/dt you need the chain rule:

    [tex]\frac{dw}{dt} = \frac{\partial w}{\partial x} \frac{dx}{dt} + \frac{\partial w}{\partial y} \frac{dy}{dt} + \frac{\partial w}{\partial z} \frac{dz}{dt}[/tex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Chain rule confusion! partial derivatives