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Product Rule

  1. Jan 26, 2009 #1
    1. The problem statement, all variables and given/known data

    y = 2a + ax

    find dy/dx

    dy/dx = a

    That is right is it not, as a is treated merly as a constant

    Now consider this question:

    Use the substitution y = vx to transform the equation:

    dy/dx = (4x+y)(x+y)/x²


    x(dv/dx) = (2+v)²

    According to the mark scheme they
    differentiate dy/dx implicitally
    y = vx
    dy/dx = x(dv/dx) + v

    BUT why have we differentitated implicitally?

    Thanks :)
  2. jcsd
  3. Jan 26, 2009 #2


    Staff: Mentor

    In your first example, a is assumed to be a constant, so dy/dx = a, as you showed.
    In your second example, both x and y are variables, and v is some function of x. In the substitution y = vx, when you differentiate the right side with respect to x, you cannot treat v as a constant as you did in the first example, so you have to use the product rule. You are assuming that both y and v are functions of x, so any differentiation has to be done implicitly.
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