How do I differentiate a pair of parametric equations?
I would guide the student through the process, as this will be far more beneficial to their learning rather than just telling them the answer. So first I'd ask what would happen if they differentiated them individually, and then guide them to the point of realising that they would have to multiply one differential by the derivative of the other (using the fractional expressions of dx/dt and dy/dt to help demonstrate that dy/dt * dt/dx = dy/dx)Then I'd give them an example to work through (if they did not have one already) - this would help them to solidify their understanding. For example, for x = 7 x 3t -2 and y = 2 x 3-t + 4, I'd help them reach the solution of dy/dx = (2ln3 x 3-t)/(7ln3 x 3t) = (2/7) x 3-2tObviously we wouldn't jump to the answer like that, it's just quite hard to properly demonstrate the steps with the space given for this question.
