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

Hi there!

Anytime you're given parametric equations to differentiate, you use the relationship whereby:

Let's start off by differentiating each equation separately, then combine the two afterwards!

Differentiating y with respect to t (dy/dt) we get:

Differentiating x with respect to t (dx/dt) we get:

Now putting everything together we get:

Hopefully this answers your question clearly! If you have any follow up questions, please feel free to ask! :)

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To differentiate the parametric equations x(t) = e^t - 1/t and y(t) = 1 - t^2 with respect to t, you differentiate each equation separately using the chain rule for x(t) and the power rule for y(t).

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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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