Not sure about derivatives, but an integrator is just a rotating disk with a ball on it, both spherical. The ball rolls over the disk from friction, and the spi

Not sure about derivatives, but an integrator is just a rotating disk with a ball on it, both spherical. The ball rolls over the disk from friction, and the spinning is the magnitude of the output integral. The input function is the position of the ball relative to the center of the disk. If the ball is at the center of the disk it doesn't move, if it moves positive the ball spins up, if it moves negative the ball spins down. The overall rotation of the ball is essentially the integral. You can also do almost this to make multipliers by varying the speed of the disk. These mechanical computers were used until the mid 1900s.