How do you differentiate the following parametric equation: # x(t)=(1-t)/e^t , y(t)=t/e^(3t) #?

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Answer 1 · 2018-07-27T21:49:30

#dy/dx=\frac{1-3t}{(t-2)e^{2t}}#

Given that

#x={1-t}/e^t\implies dx/dt={t-2}/e^t#

#y={t}/e^{3t}\implies dx/dt={1-3t}/e^{3t}#

#\therefore dy/dx#

#=\frac{dy/dt}{dx/dt}#

#=\frac{{1-3t}/e^{3t}}{{t-2}/e^{t}}#

#=\frac{1-3t}{(t-2)e^{2t}}#