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Math Help - Multivariable chain rule

  1. #1
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    Multivariable chain rule

    Could I get some guidance on this subject?

    Yfrog - vh5.jpg

    Yfrog - dsc04451z

    I thought I could do the first one by starting from the right. I figured I could replace du/ds with du/dx (dx/dt), replace dx/dt with the derivative given by the info, get e^2s and sin^2 + cos ^2 as a multiplier and end up with the left side. However, du/ds leaves cost as cost and only du/dt gives me a cos^2 so I don't get that clean 1. Am I missing something, made a great mistake, or just approaching this entirely wrongly?

    Last edited by theowne; October 8th 2009 at 08:45 PM.
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  2. #2
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    Quote Originally Posted by theowne View Post
    Could I get some guidance on this subject?

    Yfrog - vh5.jpg

    Yfrog - dsc04451z

    I thought I could do the first one by starting from the right. I figured I could replace du/ds with du/dx (dx/dt), replace dx/dt with the derivative given by the info, get e^2s and sin^2 + cos ^2 as a multiplier and end up with the left side. However, du/ds leaves cost as cost and only du/dt gives me a cos^2 so I don't get that clean 1. Am I missing something, made a great mistake, or just approaching this entirely wrongly?

    No, you can't "replace du/ds with du/dx (dx/dt)". \frac{\partial u}{\partial s}= \frac{\partial f}{\partial x}\frac{\partial x}{\partial x}+ \frac{\partial f}{\partial y}\frac{\partial y}{\partial s}
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