Question

i need help with this problem -
find dy/dx and dx/dy of the following curve:
x = t^2, y = 5 - 4t

Answer 1

You can take the derivative of each of x and y with respect to t and then combine as follows.
\[\frac{dx}{dt}=2t,\frac{dy}{dt}=-4\]Now\[\frac{dy}{dx}=\frac{dy}{dt}\frac{dt}{dx}=-4 \times \frac{1}{2t}=-\frac{2}{t}\]and\[\frac{dx}{dy}=\frac{dx}{dt}\frac{dt}{dy}=2t \times -\frac{1}{4}=-\frac{t}{2}\]which equals\[\frac{1}{\left( \frac{dy}{dx} \right)}\]incidentally.