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!

Partial derivative

  1. Dec 17, 2013 #1
    1. The problem statement, all variables and given/known data
    Hi

    Say I have a function [itex]f(x(t), t)[/itex]. I am not 100% sure of the difference between
    [tex]
    \frac{df}{dt}
    [/tex]
    and
    [tex]
    \frac{\partial f}{\partial t}
    [/tex]
    Is it correct that the relation between these two is (from the chain rule)
    [tex]
    \frac{df}{dt} = \frac{\partial f}{\partial t} + \frac{\partial f}{\partial x}\frac{dx}{dt}
    [/tex]
     
  2. jcsd
  3. Dec 17, 2013 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It is easy to be confused by the ambiguity of ##\frac{\partial f}{\partial t}## symbol. If you write the expression instead as ##f(u,v)## where ##u = x(t),~v=t## you would write$$
    \frac{df}{dt} = f_u\frac {du}{dt} + f_v\frac{dv}{dt}=f_u\frac{dx}{dt}+f_v\cdot 1$$You wouldn't normally talk about ##\frac{\partial f}{\partial t}## as though ##f## depended on another variable also. But as the chain rule gives, you need the partials of ##f## with respect to each of its arguments. If you understand that ##\frac{\partial f}{\partial x}## and ##\frac{\partial f}{\partial t}## in this setting mean the partials of ##f## with respect to its first and second arguments, you should be OK.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Partial derivative
  1. Partial derivative (Replies: 11)

  2. Partial derivative (Replies: 2)

  3. Partial derivatives (Replies: 1)

  4. Partial derivative (Replies: 21)

  5. The partial derivative (Replies: 2)

Loading...