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Math Help - Partial Differentiation

  1. #1
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    Partial Differentiation

    Find : ∂z/∂x
    <br />
z = 3x\sqrt{y} - xcos(xy)<br />

    My solution:
    Let K = xcos(xy)
    Let u = x , v = cos(xy)
    ∂u/∂x = 1
    ∂v/∂x = -ysin(xy)
    Product rule:
    ∂K/∂x = v(∂u/∂x) + u(∂v/∂x) = cos(xy) - xysin(xy)


    ∂z/∂x = 3\sqrt{y} -cos(xy) -xysin(xy)<br />
    Last edited by wkn0524; May 28th 2010 at 09:10 AM. Reason: fixed latex
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  2. #2
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    There is no need to make substitutions ..
    Fix your function please,,
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  3. #3
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    Sorry, im learning how to using Math equation...my final answer is ∂z/∂x = 3\sqrt{y} -cos(xy) -xysin(xy). Im just want to ask whether im correct or not.
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  4. #4
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    To write the square root of y : \sqrt{y}
    You need the product rule to differentiate the second term,,
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  5. #5
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    Quote Originally Posted by General View Post
    To write the square root of y : \sqrt{y}
    You need the product rule to differetiate the second term,,

    Thanks. What you mean by "the product rule to differetiate the second term".
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  6. #6
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    Quote Originally Posted by wkn0524 View Post
    <br />
z = 3x\sqrt{y} - { \color{red} xcos(xy) }<br />
    How can you differentiate the red one ?
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  7. #7
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    Quote Originally Posted by General View Post
    How can you differentiate the red one ?
    Sorry...The question is ask to find ∂z/∂x for this question <br />
z = 3x\sqrt{y} - xcos(xy)<br />

    After differentiate xcos(xy), then i get <br />
cos(xy) - xysin(xy)<br />
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  8. #8
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    I know,
    You have:
    z=3x\sqrt{y} - x \, cos(xy)

    And you want to find z_x , Right ?
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  9. #9
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    Quote Originally Posted by General View Post
    I know,
    You have:
    z=3x\sqrt{y} - x \, cos(xy)

    And you want to find z_x , Right ?
    Is ∂z/∂x = z_x ?

    If same, then yes.
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  10. #10
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    Yes.
    They are the same.

    z=3x\sqrt{y} - x \, cos(xy)

    z_x=3\sqrt{y} - \left[ { \color{blue} cos(xy) - xy sin(xy) } \right]

    I used the product in blue,,
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  11. #11
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    Quote Originally Posted by General View Post
    Yes.
    They are the same.

    z=3x\sqrt{y} - x \, cos(xy)

    z_x=3\sqrt{y} - \left[ { \color{blue} cos(xy) - xy sin(xy) } \right]

    I used the product in blue,,
    Ouch, got the minus sign. The partial differentiation was not exactly same as differentiation topic, knew the concepts now.
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