To find dy/dx, we need to use the chain rule, as we have y and x expressed in terms of t.
First, we will find dy/dt and dx/dt:
- For y = 6t, the derivative dy/dt is: dy/dt = 6
- For x = 3t², the derivative dx/dt is: dx/dt = 6t
Now, we can find dy/dx using the formula:
dy/dx = (dy/dt) / (dx/dt)
Substituting the values we found:
dy/dx = 6 / (6t) = 1/t
So, the final answer is:
dy/dx = 1/t
This expression indicates how y changes with respect to x as the parameter t varies.