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Math Help - [SOLVED] differentiation...

  1. #1
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    [SOLVED] differentiation...

    i am stuck in the end...one term does not match. otherwise the answer wud come...
    question is:
    if x^p*y^q=(x+y)^{p+q} then prove that dy/dx =y/x and d/dx(dy/dx)=0.
    please help
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  2. #2
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    Hello darachit
    Quote Originally Posted by darachit View Post
    i am stuck in the end...one term does not match. otherwise the answer wud come...
    question is:
    if x^p*y^q=(x+y)^{p+q} then prove that dy/dx =y/x and d/dx(dy/dx)=0.
    please help
    Take logs of both sides:

    p\ln x + q \ln y = (p+q)\ln(x+y)

    \Rightarrow \frac{p}{x}+ \frac{q}{y}\frac{dy}{dx}=\frac{p+q}{x+y}\left(1+\f  rac{dy}{dx}\right)

    If you now solve for \frac{dy}{dx} and simplify, the equation becomes

    \frac{dy}{dx}\Big(x(qx-py)\Big)= y(qx-py)

    \Rightarrow \frac{dy}{dx}=\frac{y}{x}

    Then \frac{d}{dx}\Big(\frac{dy}{dx}\Big) = \frac{x\frac{dy}{dx}-y}{x^2}= 0

    Grandad
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  3. #3
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    thanx ALOT!
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