Question

How do you differentiate the following parametric equation: `x(t)=(t+1)e^t, y(t)= (t-2)^2+t`?

Answer 1

`(2t-3)/(e^t t + 2e^t)`

Explanation:

`dy/dx = dy/dt / dx/dt`

since `dy/dt / dx/dt = dy/dt * dt/dx = dy/dx` (cancelling `dt` in the numerator and denominator)

`x(t) = (t+1)e^t`
`dx/dt = d/dt((t+1)e^t) = (t+1)e^t + e^t`

`y(t) = (t-2)^2 + t`
`dy/dt = d/dt((t-2)^2 + t) = 2(t-2) + 1`

Therefore,
`dy/dx = (2(t-2) + 1)/((t+1)e^t + e^t) = (2t-3)/(e^t t + 2e^t)`