Ik moet
\(\frac{ \partial ^2 f}{\partial \theta ^2}\)
vinden voor \( f(x,y)\)
waarbij \( x =r\cos\theta , y= r\sin\theta\)
Ik ben als volgt begonnen\(\frac{ \partial ^2 f}{\partial \theta ^2}= \frac{\partial}{\partial\theta}\frac{\partial f}{\partial\theta}= \frac{\partial}{\partial\theta}(-r\sin\theta\frac{\partial f}{\partial x} + r\cos\theta\frac{\partial f}{\partial y}) = -r\cos\theta\frac{\partial f}{\partial x} - r\sin\theta\frac{\partial}{\partial\theta}\frac{\partial f}{\partial x} - r\sin\theta\frac{\partial f}{\partial y} +r\cos\theta\frac{\partial}{\partial\theta}\frac{\partial f}{\partial y} \)
Nu is mijn vraag, hoe bereken ik \( \frac{\partial}{\partial\theta}\frac{\partial f}{\partial x}\)
?en \(\frac{\partial}{\partial\theta}\frac{\partial f}{\partial y}\)
?bedankt
