- Thread starter
- #1

$$

\frac{\partial u}{\partial\theta} = \frac{\partial u}{\partial x}\frac{\partial x}{\partial\theta} + \frac{\partial u}{\partial y}\frac{\partial y}{\partial\theta} = -r\sin\theta\frac{\partial u}{\partial x} + r\cos\theta\frac{\partial u}{\partial y}

$$

So taking the second derivative.

$$

\frac{\partial u}{\partial\theta} = r\left[\frac{\partial u}{\partial x}\frac{\partial }{\partial\theta}\left(-\sin\theta\frac{\partial u}{\partial x} + \cos\theta\frac{\partial u}{\partial y}\right)+\frac{\partial u}{\partial y}\frac{\partial }{\partial\theta}\left(-\sin\theta\frac{\partial u}{\partial x} + \cos\theta\frac{\partial u}{\partial y}\right)\right]

$$

What is the next step? I keep getting it wrong.