# How do you differentiate the following parametric equation: # (t-5t^3,3t^4-t^3)#?

The derivative of the parametric function is

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To differentiate the parametric equations ((x(t), y(t)) = (t - 5t^3, 3t^4 - t^3)) with respect to (t), you differentiate each component separately using the chain rule:

[\frac{dx}{dt} = \frac{d}{dt}(t - 5t^3) = 1 - 15t^2]

[\frac{dy}{dt} = \frac{d}{dt}(3t^4 - t^3) = 12t^3 - 3t^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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