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

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To differentiate the parametric equations ( x(t) = \ln(t) - t ) and ( y(t) = (t - 3)^2 ) with respect to ( t ), you can use the chain rule and basic differentiation rules:

[ \frac{dx}{dt} = \frac{d}{dt}(\ln(t) - t) = \frac{1}{t} - 1 ]

[ \frac{dy}{dt} = \frac{d}{dt}((t - 3)^2) = 2(t - 3) ]

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