How do you differentiate the following parametric equation: # (tt^3,3/t^4t^3)#?
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To differentiate the parametric equations ( x(t) = t  t^3 ) and ( y(t) = \frac{3}{t^4}  t^3 ) with respect to ( t ), use the chain rule. Here's how:

Differentiate ( x(t) = t  t^3 ) with respect to ( t ): [ \frac{dx}{dt} = 1  3t^2 ]

Differentiate ( y(t) = \frac{3}{t^4}  t^3 ) with respect to ( t ): [ \frac{dy}{dt} = \frac{12}{t^5}  3t^2 ]
Therefore, the differentiations of the given parametric equations are:
[ \frac{dx}{dt} = 1  3t^2 ]
[ \frac{dy}{dt} = \frac{12}{t^5}  3t^2 ]
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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