1. Limited time only! Sign up for a free 30min personal 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: y = f(t, t^2, t^3) and y = g(t, h(t), k(t^2))

  1. Mar 30, 2014 #1

    939

    User Avatar

    1. The problem statement, all variables and given/known data

    I am confused because for each problem there is no equation and for one no intermediate variables.

    Compute dy/dt when

    a) y = f(t, t^2, t^3)
    b) y = g(t, h(t), k(t^2))

    2. Relevant equations

    a) y = f(t, t^2, t^3)
    b) y = g(t, h(t), k(t^2))

    3. The attempt at a solution

    a)
    З1.jpg
    dy/dt = ∂f/∂t * ∂f/∂t^2 * ∂f/∂t^3


    2) з2.jpg

    dy/dt = ∂f/∂t + (∂g/∂h * dh/dt) + (∂g/∂k * dk/dt^2)
     
    Last edited: Mar 30, 2014
  2. jcsd
  3. Mar 30, 2014 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    There are intermediate variables, they are just implied so you don't see them. For a) think of ##u = t,~v = t^2,~w=t^3## and ##y = f(u,v,w)##. Now do you see how to calculate ##\frac{dy}{dt}## using the chain rule?
     
  4. Mar 30, 2014 #3

    939

    User Avatar

    Does this work?
    Без імені.jpg
    dy/dt = (∂y/∂u * du/dt) + (∂y/∂v * du/dt^2) + (∂y/∂w * dw/dt^3)
     
  5. Mar 30, 2014 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Look up that chain rule in your calculus book. Is that what it says?
     
  6. Mar 31, 2014 #5

    939

    User Avatar

    Sorry... If it was i.e. y = (x, y), x = (t), y = (t^2) I would get it and there my book says you do the same steps as I listed above.

    I'm just not sure here... y = f(t, t^2, t^3). Thus, y = dependent. t, t^2, t^3 are independent. Intermediate variables must connect the two... If that is not it, maybe just find derivatives f t, t^2 and t^3 in the equation?
     
  7. Mar 31, 2014 #6

    Mark44

    Staff: Mentor

    Yes. Using LCKurtz's suggestion these would be du/dt, dv/dt, and dw/dt.
     
  8. Mar 31, 2014 #7

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You likely calculated them correctly but I was pointing out your notation was bad. Those two red factors should be dv/dt and dw/dt. The u was probably a typo but you shouldn't have t^2 and t^3 in the formulas.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted