given that x = 2at² and y = 4at, find dy/dx as the 1st derivative; dy/dx= dy/dt × dt/dx => dx/dt = 4at and so dt/dx = 1/(4at) Also dy/dt = 4a. Hence, dy/dx = 4a × 1/4at = 1/t Finding the 2nd Derivative we have; d²y/dx²=d/dx[dy/dx] => d²y/dx² = d/dt (1/t) × dt/dx = -1/t²×1/4at