Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Total derivative and partial derivative

  1. Aug 18, 2014 #1
    can anyone tell me the difference of application of total derivative and partial derivative in physics?
    i still can't figure it out after searching on the internet
     
  2. jcsd
  3. Aug 18, 2014 #2

    ShayanJ

    User Avatar
    Gold Member

    A total derivative tells you how a quantity changes if another quantity changes, regardless on the kind of dependence of the first quantity on the second. But for a partial derivative, the second quantity should only appear explicitly in the expression giving the first quantity.
    For example consider [itex] y(x(t),t)=2x(t)^2+bt^2 [/itex], we'll have:
    [itex]
    \frac{\partial y}{\partial t}=2bt \\
    \frac{d y}{dt}=4x(t) \frac{dx(t)}{dt}+2bt
    [/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook