Question

How do you differentiate the following parametric equation: `x(t)=-t-e^t, y(t)= -2t^2-2t^3e^(t)`?

Answer 1

`:. dy/dx` = `(y'(t))/(x'(t)` = `{(1+e^t)}/{2t(2+3te^t+t^2e^t)}.`

Explanation:

`x(t)=-t-e^t rArr x'(t)=-1-e^t =-(1+e^t).`
`y(t)=-2t^2-2t^3e^t rArr y'(t)=-4t-2{3t^2e^t+t^3e^t}=-2t(2+3te^t+t^2e^t).`

Now, by the Rule for Parametric Differentiation,

`:. dy/dx` = `(y'(t))/(x'(t)` = `{(1+e^t)}/{2t(2+3te^t+t^2e^t)}.`