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Need help with differentiation.

  1. Feb 9, 2008 #1
    f(x,y)=e2x*ln(x/y^2)

    find f(subscript-x)

    Can anyone help me with this differentiation please? I know you must treat y as a constant and differentiate with respect to x.
     
  2. jcsd
  3. Feb 9, 2008 #2

    HallsofIvy

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    Just do it step by step. Since it is a product of two functions, use the product rule:
    [itex]f_x= (e^{2x})_x (ln(x/y^2))+ (e^{2x})(ln(x/y^2))_x[/itex]

    Now do [itex](e^{2x})_x[/itex] alone: the derivative of [itex]e^x[/itex] is just [itex]e^x[/itex] so by the chain rule the derivative is [itex]e^{2x}(2x)_x= 2e^{2x}[/itex].

    Next do [itex](ln(x/y^2))_x[/itex] alone: the derivative of ln(x) is 1/x so by the chain rule the derivative is [itex](y^2/x)(x/y^2)_x= (y^2/x)(1/y^2)= 1/x[/itex].

    Actually, that last could be done more easily: since [itex]ln(x/y^2)= ln(x)- 2ln(y)[/itex], the derivative is just 1/x.

    Now put them all together.
     
  4. Feb 9, 2008 #3
    Thanks very much I understand now
     
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