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Math Help - Partial Derivatives

  1. #1
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    [SOLVED]Partial Derivatives

    Hi,

    For this equation sinxy+sinyz+sinxz=1,
    how do I find Partial Derivatives-.jpgandPartial Derivatives-2.jpg?

    Thanks
    Last edited by esum0209; October 10th 2010 at 11:40 AM.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by esum0209 View Post
    Hi,

    For this equation sinxy+sinyz+sinxz=1,
    how do I find Click image for larger version. 

Name:	未命名.JPG 
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ID:	19254andClick image for larger version. 

Name:	未命名2.JPG 
Views:	22 
Size:	1.1 KB 
ID:	19255?

    Thanks
    This requires you to use implicit partial differentiation. So given \sin xy+\sin yz+\sin xz=1, partially differentiate both sides wrt x:

    \begin{aligned} &\frac{\partial}{\partial x}\sin xy+ \frac{\partial}{\partial x}\sin yz+\frac{\partial}{\partial x}\sin xz=\frac{\partial}{\partial x}1\\ \implies & y\cos xy+y\frac{\partial z}{\partial x}\cos yz+\left(z+x\frac{\partial z}{\partial x}\right)\cos xz=0\end{aligned}

    At this stage, you can now solve for \dfrac{\partial z}{\partial x}.

    You can do something similar in finding \dfrac{\partial z}{\partial y}.

    Can you take it from here?
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  3. #3
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    Thank you, I get it now
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