If x = 3t² and y = 6t, how do you find dy/dx?

To find dy/dx given the equations for x and y in terms of t, we can use the chain rule of calculus. This process involves finding the derivatives of x and y with respect to t and then using those derivatives to find dy/dx.

First, we differentiate both x and y with respect to the parameter t:

• For x:

  x = 3t²
          dx/dt = d(3t²)/dt = 6t

• For y:

  y = 6t
          dy/dt = d(6t)/dt = 6

Now that we have dx/dt and dy/dt, we can find dy/dx using the chain rule:

Using the formula:

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

Substituting the values we found:

dy/dx = 6 / (6t)

Thus, simplifying this gives:

dy/dx = 1/t

In conclusion, the derivative of y with respect to x, given the functions x and y in terms of t, is:

dy/dx = 1/t