How do you differentiate the following parametric equation: x(t)=-2te^t+4t, y(t)= -2t^2-3e^(t) ?

1 Answer
Jul 12, 2017

the first derivative, dy/dx = dy/dt/dx/dt for parametric equations
the reason this holds true could be seen by treating dy, dx, and dt as differentials (which they are) and upon dividing, dt cancels out and you are left with dy/dx

as a refresher, d/dt(x^t) = tx^(t-1) and d/dt(e^t) = e^t * t'

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dy/dt = d/dt (-2t^2 - 3e^t) = -4t - 3e^t

dx/dt = d/dt (-2te^t + 4t) = -2(e^t + te^t) + 4

= -2e^t - 2te^t + 4

dy/dx = dy/dt/dx/dt = (-4t - 3e^t)/(-2e^t - 2te^t + 4)