What is dy/dx if x=5t^3 and y=3t^5?

y = 3t^5

x
=5t^3.

Here both x and y are expressed in terms of t. This
is called the parametric equation of the curve .

Therefore
dy/dx  = (dy/dt)* dt/dx.  . Or

dy/dx =
(dy/dt)/(dx/dt)

y = 3t^5. So dy/dt = (3t^5)' = 3*5*t^(5-1)
= 15t^4.

x =5t^3 . So  dx/dt = (5t^3)' = 5*3t^(3-1) =
15t^2.

Therefore dy/dx = (dy/dt)/(dx/dt) = 15t^4/(15t^2) =
t^2.

Therefore dy/dx = t^2 .