The total derivative may be used in dynamic geometry. See Geogebra. The addition of time to geometry was a part of Newton's calculus. The static $(x,y,z)$ coordinate system expanded to $(x,y,z,t)$. The static coordinates expanded to $[x(t),y(t),z(t)]$. One derivative of interest is $dz/dt$. The independent variable is time which is plotted along the $x$-axis. The dependent variables $(x,y,z)$ are plotted individually along the vertical axis. Also, in geometry $z$ may be plotted as the radius of an expanding circle $x(t)^2 + y(t)^2 = z(t)^2$. This adds time to the Pythagorean theorem. In special relativity $z=ct$ where $c$ is the speed of light. This geometry is the light cone. Newton was interested in the orbits of planets. This requires keeping track of the directions of motions with vectors. Fortunately the motion of the earth is mostly in a plane. In this case the object in plane geometry is the ellipse for closed orbits. It is a hyperbola or parabola for open orbits. Another geometric item of interest is the curvature. For a circle it is $1/r$ and for a sphere it is $1/r^2$. The $1/r^2$ is interpreted as the gravitational force. Euler proved that the second derivative with respect to time is also the curvature. This second derivative is interpreted as the acceleration. Thus Newton's second law states that temporal curvature must be equal to spatial curvature using local masses and a universal constant as parameters. This was the dynamic geometry that was used before Einstein created his geometry of gravity, known as General Relativity. Quantum mechanics required the development of a completely different type of geometry.