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

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To differentiate the parametric equations ( x(t) = te^{-t} ) and ( y(t) = \frac{e^t}{t} ) with respect to ( t ), you apply the chain rule and quotient rule, respectively.

( \frac{dx}{dt} = e^{-t} - te^{-t} )

( \frac{dy}{dt} = \frac{te^t - e^t}{t^2} )

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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