If dy/dx=1/t find d^2y/dx^2

Question

If x=at^2 ,y=2at, find dy/dx and d^2y/dx^2 in terms of t

Answer 1

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

d²y/dx² = d/dx(1/t) = d/dt(1/t)·dt/dx = (- 1/t²)/(dx/dt) = (-1/t²)/(2at) = -1/(2at³)