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Math Help - Differentation Question

  1. #1
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    Differentation Question

    Hi everyone

    Need help on this question, can someone help me.Really appreciate all help & support.

    Find \frac {dz}{dx} & \frac{dz}{dy} for
    xyz-3yz^2-4xy^2=0

    Thank you in advance for all help & support.
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  2. #2
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    Just in case a picture helps...



    ... where



    ... is the product rule, and...



    ... the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

    Follow through by solving the bottom row for \frac{\partial z}{\partial x} , of course.

    w.r.t. y ...



    Spoiler:

    _________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Last edited by tom@ballooncalculus; March 9th 2010 at 01:42 AM. Reason: tiny typo
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  3. #3
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    thank you for replying. really hope someone can help with the working then i'll understand better.

    thank you for all help & support,really appreciate.
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  4. #4
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    Quote Originally Posted by anderson View Post
    Hi everyone

    Need help on this question, can someone help me.Really appreciate all help & support.

    Find \frac {dz}{dx} & \frac{dz}{dy} for
    xyz-3yz^2-4xy^2=0

    Thank you in advance for all help & support.
    Differentiate both sides of the equation with respect to x
    (treating z as a function of x and y as a constant):

    (xyz)_x- (3yz^2)_x- (4xy^2)_x= 0
    = yz+ xyz_x- 6yz z_x- 4y^2= 0

    Now solve for z_x

    Differentiat both sides of the equation with respect to y
    (treating z as a function of y and x as a constant):
    (xyz)_y- (3yz^2)_y- (4xy^2)_y= 0

    You finish that.
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  5. #5
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    thank you for explaining, just wondering how we get the xyz_x.

    thank you so much for all help & support.
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  6. #6
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    hi everyone

    thank you for guiding. is this correct, please help confirm.thank you for helping me to learn, really appreciate all help & support.

    <br /> <br />
xyz-3yz^2-4xy^2=0<br />
    yz+xy\frac{dz}{dx}-6yz\frac{dz}{dx}-4y^2
    \frac{dz}{dx}(xy-6yz)=4y^2-yz
    \frac{dz}{dx}=\frac{4y^2-yz}{xy-6yz}

    xz+xy\frac{dz}{dy}-3z^2-6yz\frac{dz}{dy}-8xy=0
    \frac{dz}{dy}(xy-6yz)=3z^2+8xy-xz
    \frac{dz}{dy}=\frac{3z^2+8xy-xz}{xy-6yz}
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  7. #7
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    Correct
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