Question

x=a/t² y=bt,Find dy/dx :(Wherever y is defined as a function of x and dx/dt or dx/dθ≠0)

Answer 1

x = a/t² => x = at^-2

differentiate with respect to t,

dx/dt = d{at^-2}/dt

dx/dt. = -2at^-3 = -2a/t³ .....(1)

again, y = bt

differentiate with respect to t,

dy/dt = d{bt}/dt = b ............(2)

now, dy/dx = {dy/dt}/{dx/dt}

= b/{-2a/t³}

= bt³/-2a

hence, dy/dx = bt³/-2a

Answer 2

In the attachment I have answered this problem.        I have applied parametric differentiation to find derivative of the given function.     See the attachment for detailed solution.