We all know that, assuming [tex]x(t) =[/tex] position as a function of time, then: [tex]x'(t) = v(t) = velocity[/tex] [tex]x''(t) = v'(t) = a(t) = acceleration[/tex] [tex]x'''(t) = v''(t) = a'(t) = j(t) = jerk[/tex] (assuming j is the symbol for jerk). But what does [tex]x''''(t) = j'(t)[/tex] come out to be? Is there a fourth derivative of position? And if so, is it ever practically used? What about fifth, sixth, seventh, etc derivatives? This is just something I've been extremely curious about since I learned of the third derivative, jerk (or jolt). Thanks!!