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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!