Question

How do you differentiate the following parametric equation: `x(t)=-te^t+t, y(t)= 3t^3-4t`?

Answer 1

`frac{dy}{dx} = frac{9t^2 - 4}{1 - (t + 1)e^t}`

Explanation:

`frac{dx}{dt} = 1 - (t + 1)e^t`

`frac{dy}{dt} = 9t^2 - 4`

Using the Chain Rule,

`frac{dy}{dx} = frac{ frac{dy}{dt} }{ frac{dx}{dt} }`

`= frac{9t^2 - 4}{1 - (t + 1)e^t}`