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!

Homework Help: Implicit Differentiation w/ Composite Function

  1. Oct 31, 2009 #1
    1. The problem statement, all variables and given/known data

    Given the equation y= f(x) , at a certain point the slope of the curve is 1/2 and the x-coordinate decreases at 3 units/s. At that point, how fast is the y-coordinate of the object changing?

    3. The attempt at a solution

    Dy/dx = f ' (x) dx/dt

    Would that be the correct way to begin this problem? Then plug in 3 for dx/dt and 1/2 for f'(x)?

  2. jcsd
  3. Oct 31, 2009 #2


    Staff: Mentor

    Not quite.
    You have
    y = f(x), where both y and x are assumed (implicitly) to be functions of t. I could write this as y(t) = f(x(t)), which would make the dependence of y and x on t explicit

    dy/dt = d/dt(f(x(t)) = f'(x(t)) dx/dt
    Here I have used the chain rule.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook