This is a really simple question, but I haven't found an answer anywhere.
The gradient of a vector $\vec{f}=<x(t),y(t),z(t)>$ is denoted by $\vec{\triangledown f}=<x'(t),y'(t),z'(t)>$. Is there a symbol for the vector $<x''(t),y''(t),z''(t)>$?
Thanks.
What you wrote is the derivative of a vector with respect to $t$. The gradient of $f(x,y,z)$ in cartesian coordinates is $$\nabla f = \left( \frac{\partial f} {\partial x} , \frac{\partial f} {\partial y} ,\frac{\partial f} {\partial z} \right)$$
The thing that maybe you are asking for is the Laplacian, which depending on the book is written as $\nabla ^2 f$ or $\Delta f$ and, in cartesian coordinates, it is $$\nabla^2 f = \left( \frac{\partial ^2 f} {\partial x ^2} , \frac{\partial ^2 f} {\partial y^2} ,\frac{\partial ^2 f} {\partial z^2} \right)$$