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Math Help - Partial Derivative Simplification.

  1. #1
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    Partial Derivative Simplification.

    The following image shows my confusion:



    I don't have any trouble doing the derivative, but how did they arrive from the second-last line to the last?

    I know that sin^2(x) + cos^2(x) = 1, but I can't see how to relate that here.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by scorpion007 View Post
    The following image shows my confusion:



    I don't have any trouble doing the derivative, but how did they arrive from the second-last line to the last?

    I know that sin^2(x) + cos^2(x) = 1, but I can't see how to relate that here.
    Since you were told that {\color{red}x}={\color{red}r\cos\theta} and {\color{blue}y}={\color{blue}r\sin\theta}, we see that:

    y\left(-{\color{blue}r\sin\theta}\right)+x\left({\color{re  d}r\cos\theta}\right)=y\left(-{\color{blue}y}\right)+x\left({\color{red}x}\right  )=x^2-y^2
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  3. #3
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    Ahh! Oops. Of course Thank you.
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