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

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Answer 1 · 2018-02-18T19:25:18

#dy/dx=(-2t^2)/lnt(4+2t^2e^t(t+3))#

#dy/dx=(dy/dt)/(dx/dt)#

#x=(lnt)^2#

#dx/dt=2(lnt)(1/t)=2/tlnt#

#y=-2t^2-2t^3e^t#

#d/dt(e^tf(t)=e^t(f(t)+f'(t))#

#f(t)=t^3, f'(t)=3t^2#

#dy/dt=-2xx2t-2xx(e^t(t^3+3t^2))=-4t-2e^t(t^3+3t^2)#

#dy/dx=(-4t-2e^t(t^3+3t^2))/(2/tlnt)#

#dy/dx=-(t(4+2t^2e^t(t+3))/(2/tlnt))#

#dy/dx=(-2t^2)/lnt(4+2t^2e^t(t+3))#