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'#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#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)#