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Partial Derivatives (Chain Rule)

  1. Dec 5, 2004 #1
    Original question:

    Let w = y^2 + xz. If x = rcos(theta), y = rsin(theta), and z = z, find (partial w)/(partial r) and (partial w)/(partial theta).

    Could someone please check my answers?

    (partial w)/(partial r) = zcos(theta) + 2ysin(theta)

    (partial w)/(partial theta) = -rzsin(theta) + 2rycos(theta)

    Thank you!
  2. jcsd
  3. Dec 5, 2004 #2


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    The results are outstanding.They would be perfect if u replaced in the RHS of each equality "x" and "y" through their new definitions.Only that way it could be said u made a change of variable and in the differentiations u took it into consideration.
  4. Dec 5, 2004 #3
    Looks correct. Usually when dealing with cylindrical coors, one converts all variables over. Meaning, it is a bit easier to convert all x's and y's to cylindrical coors then do the partial derivatives.
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