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

1 Answer
Aug 31, 2016

dx/dt = (e^t)/(4t^2) - (e^t)/(2t^3) - 1, dy/dt = 1 - e^t

Explanation:

Because the curve is expressed in terms of two functions of t we can find the answer by differentiating each function individually with respect to t. First note that the equation for x(t) can be simplified to:

x(t) = 1/4 e^t 1/(t^2) - t

While y(t) can be left as:

y(t) = t - e^t

Looking at x(t), it is easy to see that the application of the product rule will yield a quick answer. While y(t) is simply standard differentiation of each term. We also use the fact that d/dx e^x = e^x.

dx/dt = (e^t)/(4t^2) - (e^t)/(2t^3) - 1

dy/dt = 1 - e^t