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

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Answer 1 · 2018-02-03T08:38:03

#(dy)/(dx)=(e^t(t+1)-1)/(2e^t(t+1)+4t)#

For a parametric function #f(x(t),y(t))#, #(dy)/(dx)=((dy)/(dt))/((dx)/(dt))#

As #x(t)=-te^t+t#,

#(dx)/(dt)=-(te^t+1*e^t)+1=1-e^t(t+1)#

and as #y(t)=-2t^2-2te^t#, #(dy)/(dt)=-4t-2(te^t+1*e^t)#

= #-4t-2e^t(t+1)#

Hence, #(dy)/(dx)=(1-e^t(t+1))/(-4t-2e^t(t+1))#

= #(e^t(t+1)-1)/(2e^t(t+1)+4t)#