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Homework Help: Quick question on differentiation

  1. Feb 20, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the value of the following derivative at x=1:


    where u(1)=3, u'(1)=-4, v(1)=-2, v'(1)=5

    3. The attempt at a solution

    Differentiating the equation:

    [(u)(2v') - (u')(2v)]/(u^2)

    plugging in the values i get 14/9 as the value.

    now my question arises from the derivative of 2v. Would it be just 2? or 2v' as v represents a 'complex base' (therefore using the chain rule)??

    the question seems simple enough to me aswell but i just want to clarify this.

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

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Feb 20, 2010 #2


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    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi g$up! Welcome to PF! :wink:
    The derivative (wrt x) of 2v is definitely 2v'. :smile:
  4. Feb 20, 2010 #3


    Staff: Mentor

    To expand on what tiny-tim said, d/dv(2v) = 2, but with d/dx(2v) there's a tacit assumption that v is a function of x, so d/dx(2v) = 2dv/dx = 2v'. In this problem, both u and v are assumed to be differentiable functions of x.
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