given that $z=f(x,y)$ and $x =r\cos(\theta)$ and y = $r\sin(\theta)$
$d^2(z)/d(r)^2$ and $d^2(z)/d(r)$
are both second derivatives of the function $z$? I am getting a little confused with all the notations.
given that $z=f(x,y)$ and $x =r\cos(\theta)$ and y = $r\sin(\theta)$
$d^2(z)/d(r)^2$ and $d^2(z)/d(r)$
are both second derivatives of the function $z$? I am getting a little confused with all the notations.
The notation for the first means $ \frac{\partial^2 z}{\partial r^2} = \frac{\partial}{\partial r} \left( \frac{\partial z}{\partial r} \right),$ so you take the partial derivative with respect to $r$ of the partial derivative of $z$ with respect to $r$, hence the "second derivative" of $z$ with respect to $r$.
The notation for the second quantity does not make sense, at least not according to anything I'm familiar with.