Results 1 to 2 of 2

Math Help - a quick question about partial derivatives

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    19

    a quick question about partial derivatives

    When you take the partial derivative of

    z=x^2y + xy^2 , x=2+t^4 , y= 1-t^3

    you get 4(2xy+y^2)t^3 - 3(x^2+2xy)t^2

    do you have to plug "2+t^4" in for each x and "1-t^3" in for each y?

    Why or why not?

    I was under the assumption that you needed to leave the answer in the same variable, in this case "t".
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Dec 2008
    Posts
    319
    In our case, we are calculating not a partial derivative of z but the ordinary derivative of z with respect to t. To answer your question, we don't have to replace x and y with expressions for t if we regard them as functions of t, as long as we remember that

    \frac{dz}{dt}=\frac{\partial z}{\partial x}\frac{dx}{dt}+\frac{\partial z}{\partial y}\frac{dy}{dt}

    is a function of one variable, t.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: May 28th 2011, 01:30 PM
  2. quick question about partial sign
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 23rd 2010, 12:00 PM
  3. Quick Question on Partial Fractions Problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 26th 2010, 09:49 PM
  4. Directional derivatives - quick question
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 26th 2009, 09:20 AM
  5. Replies: 5
    Last Post: September 16th 2008, 02:30 AM

Search Tags


/mathhelpforum @mathhelpforum