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    Please help me with this C3 question!

    Question:
    (b) The curve C has the Cartesian equation y=3^(x-1)
    By writing lny in terms of x, find an expression for dy/dx in terms of x.

    Answer:
    y = 3x-1
    so lny = (x - 1)ln3
    1/y dy/dx = ln3
    So dy = yln3 dx
    = (3x-1)ln3

    I understand the first stage but I'm not sure how they've got to 1/y dy/dx = ln3 and where the x-1 has gone.
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    (Original post by PuffyPenguin)
    Please help me with this C3 question!

    Question:
    (b) The curve C has the Cartesian equation y=3^(x-1)
    By writing lny in terms of x, find an expression for dy/dx in terms of x.

    Answer:
    y = 3x-1
    so lny = (x - 1)ln3
    1/y dy/dx = ln3
    So dy = yln3 dx
    = (3x-1)ln3

    I understand the first stage but I'm not sure how they've got to 1/y dy/dx = ln3 and where the x-1 has gone.
    Note that (x-1)\ln(3)=x\ln(3)-\ln(3) then differentiate this w.r.t x. Remember that \ln(3) is just a constant number.
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    (Original post by RDKGames)
    Note that (x-1)\ln(3)=x\ln(3)-\ln(3) then differentiate this w.r.t x. Remember that \ln(3) is just a constant number.
    Okay.. but why is it 1/y dy/dx?
    That make sense though, so thanks
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    (Original post by PuffyPenguin)
    Okay.. but why is it 1/y dy/dx?
    That make sense though, so thanks
    Do you know how implicit differentiation works?

    You essentially differentiate the LHS here w.r.t y then multiply the result by dy/dx.
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    (Original post by RDKGames)
    Do you know how implicit differentiation works?

    You essentially differentiate the LHS here w.r.t y then multiply the result by dy/dx.
    No, I don't think I've covered implicit differentiation - thanks very much for the explanation
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    (Original post by PuffyPenguin)
    No, I don't think I've covered implicit differentiation - thanks very much for the explanation
    You can avoid implicit diff. by differentiating LHS w.r.t y and the RHS w.r.t x when you get to the line \ln(y)=(x-1)\ln(x), which is the expected method you're supposed to use if you haven't covered implicit diff, I suppose.
 
 
 
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