Question

How do you differentiate the following parametric equation: `x(t)=-2te^t+4t, y(t)= -5t^2-e^(t)`?

Answer 1

`(dx)/(dt) = 4 - 2(1 + t)e^t`
`(dy)/(dt) = -10t - e^t`
`dy/dx = (4 - 2(1 + t)e^t)/(-10t - e^t)`

Explanation:

Given:
`x(t) = 4t - 2te^t`
`y(t) = -5t^2 - e^t`

Differentiate both:

`(dx)/(dt) = 4 - 2(1 + t)e^t`
`(dy)/(dt) = -10t - e^t`

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

`dy/dx = (4 - 2(1 + t)e^t)/(-10t - e^t)`