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!

Derivative of Composition Functions Problem

  1. Oct 14, 2009 #1
    1. The problem statement, all variables and given/known data

    f and g are differentiable functions that have the following properties:
    i. f(x) < 0 for all values of x
    ii. g(5) = 2

    If h(x)= f(x) / g(x) and h'(x) = f '(x) / g(x), then g(x) = _____?





    2. Relevant equations

    Quotient Rule with f(x) and g(x)

    3. The attempt at a solution
    I have no idea where to begin on this problem.
    Would I first solve the derivative of h(x)?

    so h'(x) = f '(x)*g(x) - f(x)*g'(x) / (g(x))2
    then set that equal to the second given (h'(x))= f'(x)/g(x)?

    Would that be a correct way to start?
     
  2. jcsd
  3. Oct 14, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    if you mean equate the two expressions
    h'(x) = f '(x)*g(x) - f(x)*g'(x) / (g(x))^2 = f '(x)*g(x)

    then yes, sounds good
     
  4. Oct 14, 2009 #3
    From there,I have no idea where to go next. would the answer to g(x) be an actual number of a function?
     
  5. Oct 14, 2009 #4

    Mark44

    Staff: Mentor

    Unless g(x) is a constant function, its formula will never be just a number. g(2), for example, would be a number, but g(x) will be a formula that gives the output for an arbitrary input number x.
     
  6. Oct 14, 2009 #5

    lanedance

    User Avatar
    Homework Helper

    so if h'(x) = f '(x)*g(x) - f(x)*g'(x) / (g(x))^2 = f '(x)*g(x)
    then

    h'(x) - f '(x)*g(x) = - f(x)*g'(x) / (g(x))^2 = 0

    so the term f(x)*g'(x) / (g(x))^2 is zero for all x, you know f(x) <0 for all x, so this is always non-zero, g(5)=2 so this is non-zero for at least one x, what does this tell you about g'(x)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Derivative of Composition Functions Problem
Loading...