teach me some shortcuts in parametric differentiation.

When 'x' and 'y' are expressed in a single parameter, suppose 't', to find dy/dx we proceed as follows:

step 1. Find dy/dt

step 2. Find dx/dt

step 3. dy/dx = (dy/dt) / (dx/dt)

Example: x=at²; y=2at

dy/dt = 2a

dx/dt = 2at

dy/dx = (dy/dt) / (dx/dt) = 2a / 2at = 1/t