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Math Help - weird implicit differentiation problem

  1. #1
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    weird implicit differentiation problem

    Use implicit differentiation to find dy/dx if cos xy = 2x -3y.

    My steps :

    (-sin(xy))(x(dy/dx) + y) = 4x - 3(dy/dx)

    (-sin(xy))(x(dy/dx) + y) + 3(dy/dx) = 4x

    -xsin(xy)(dy/dx) - ysin(xy) + 3(dy/dx) = 4x

    -xsin(xy)(dy/dx) + 3(dy/dx) = 4x + ysin(xy)

    dy/dx (3 - xsin(xy)) = (4x +ysin(xy))

    dy/dx = (4x +ysin(xy)) / (3 - xsin(xy))


    Are my steps correct? I am not sure of the answer, cuz it looks super weird.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by h4hv4hd4si4n View Post
    Use implicit differentiation to find dy/dx if cos xy = 2x -3y.

    My steps :

    (-sin(xy))(x(dy/dx) + y) = 4x - 3(dy/dx)

    (-sin(xy))(x(dy/dx) + y) + 3(dy/dx) = 4x

    -xsin(xy)(dy/dx) - ysin(xy) + 3(dy/dx) = 4x

    -xsin(xy)(dy/dx) + 3(dy/dx) = 4x + ysin(xy)

    dy/dx (3 - xsin(xy)) = (4x +ysin(xy))

    dy/dx = (4x +ysin(xy)) / (3 - xsin(xy))


    Are my steps correct? I am not sure of the answer, cuz it looks super weird.
    You're correct!!

    These implicit differentiation problems tend to have solutions that look like this (and sometimes worse! ).
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  3. #3
    Senior Member MacstersUndead's Avatar
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    I got the same answer, but I really need to refresh my memory on this topic. Thanks for the review. :P
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  4. #4
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    thanks for your help
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  5. #5
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    Hello, h4hv4hd4si4n!

    Use implicit differentiation to find \tfrac{dy}{dx}\text{ if }\cos(xy) \:=\: 2x^2 -3y

    My steps:

    -\sin(xy)\,\left(x\tfrac{dy}{dx} + y\right) \;= \;4x - 3\tfrac{dy}{dx}

    -x\sin(xy)\tfrac{dy}{dx} - y\sin(xy) \;=\; 4x - 3\tfrac{dy}{dx}

    -x\sin(xy)\tfrac{dy}{dx} + 3\tfrac{dy}{dx} \;=\; 4x + y\sin(xy)

    \tfrac{dy}{dx}\left[3 - x\sin(xy)\right] \;=\;4x +y\sin(xy)

    . . . \frac{dy}{dx} \;=\; \frac{4x +y\sin(xy)}{3 - x\sin(xy)}

    Are my steps correct?

    Absolutely! . . . Lovely work!

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