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

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.