Partial Derivatives (Chain Rule)

[DeadxBunny]

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!

 

[dextercioby]

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.

 

[jisland85]

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.