# How do you differentiate the following parametric equation: # x(t)=t-e^(t^2-t+1), y(t)= te^(t-t^2)#?

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To differentiate the parametric equations ( x(t) = t - e^{t^2 - t + 1} ) and ( y(t) = t e^{t - t^2} ) with respect to ( t ), you can use the chain rule and the product rule.

The derivatives are as follows:

[ \frac{dx}{dt} = 1 - \left(2t - 1\right) e^{t^2 - t + 1} ]

[ \frac{dy}{dt} = e^{t - t^2} + t \left(1 - 2t\right) e^{t - t^2} ]

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