I don't understand why the following is true : We have using the chain rule :
$$\frac{\partial}{\partial x}=\frac{\partial}{\partial r}\frac{\partial r}{\partial x}+\frac{\partial}{\partial \theta}\frac{\partial \theta}{\partial x}$$
But then why :
$$\frac{\partial}{\partial x} \frac{\partial}{\partial x} = \frac{\partial^2}{\partial x^2} = (\frac{\partial}{\partial r}\frac{\partial r}{\partial x}+\frac{\partial}{\partial \theta}\frac{\partial \theta}{\partial x})^2$$ ?
Normally it should be :
$$\frac{\partial^2}{\partial x^2} = \frac{\partial}{\partial x} (\frac{\partial}{\partial r}\frac{\partial r}{\partial x}+\frac{\partial}{\partial \theta}\frac{\partial \theta}{\partial x}) = \frac{\partial}{\partial x}\frac{\partial}{\partial r}\frac{\partial r}{\partial x}+\frac{\partial}{\partial x}\frac{\partial}{\partial \theta}\frac{\partial \theta}{\partial x}$$
?
I really don't understand what is going on...
Thank you !