If x = 3t² and y = 6t, then what is dy/dx?

Solution:

x and y are the parametric functions with the parameter t.

Hence my parametric differentiation, we have dy/dx = dy/dt . dt/dx

dy/dt =  d(6t)/dt = 6

dx/dt = d(3t²)/dt = 6t

dy/dx = (dy/dt) /  dx/dt = 6/6t

dy/dx = 1/t

Let us take another example where 

x = t² - 2t  and y = t⁴ - 4t

dx/dt = 2t - 2 = 2(t - 1)

dy/dt = 4t³ - 4 = 4(t³ - 1)

dy/dx = (dy/dt) / dx/dt =   3(t³ - 1) / 2(t + 1) = (3(t - 1)(t² + t + 1)) / 2(t-1)

=  (3/2)(t² + t + 1)

If x = 3t² and y = 6t, then what is dy/dx?

Summary:

 If x = 3t² and y = 6t, then  dy/dx is 1/t