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Homework Help: Need calc help 1 last time.

  1. Jul 15, 2005 #1
    hi there i am having trouble on the following question.

    1. ln(x+y) = e^3x
    (1/x+y)(1+(dy/dx)) = (e^3x)(3)
    what can u substititue for y???
     
    Last edited: Jul 15, 2005
  2. jcsd
  3. Jul 15, 2005 #2

    lurflurf

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    Homework Helper

    I take it you are finding dy/dx by implict differentiation?
    [tex]\log(x+y)=e^{3x}[/tex]
    differentiation yeilds
    [tex]\frac{1+\frac{dy}{dx}}{x+y}=3e^{3x}[/tex]
    solving for dy/dx
    [tex]\frac{dy}{dx}=3(x+y)e^{3x}-1[/tex]
    observe x+y=exp(exp(3x))
    [tex]\frac{dy}{dx}=3e^{e^{3x}}e^{3x}-1[/tex]
    simplify
    [tex]\frac{dy}{dx}=3e^{3x+e^{3x}}-1[/tex]
    observe that one could solve the original equation for y and obtain a more straitforward solution.
    [tex]\log(x+y)=e^{3x}[/tex]
    solve for y
    [tex]y=e^{e^{3x}}-x[/tex]
    differentiate
    [tex]\frac{dy}{dx}=3e^{e^{3x}}e^{3x}-1[/tex]
     
  4. Jul 15, 2005 #3
    You're not meant to do people's work for them :/.
     
  5. Jul 15, 2005 #4
    how do u get e^e^3x
     
  6. Jul 15, 2005 #5
    By solving the natural log.
     
  7. Jul 15, 2005 #6
    ok thanks guys.
     
  8. Jul 15, 2005 #7

    HallsofIvy

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    Science Advisor

    In general, however, when doing an implicit differentiation, it is not necessary nor desirable to solve for y and then substitute that for y in the expression for the derivative. It is better to leave it in terms of both x and y.
     
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