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

# dy/dx = (cost -tsint - 2tsintcost-sin^2t) / (e^t(sint+cost)) #

We have:

By the chain rule we have:

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To differentiate the given parametric equations ( x(t) = e^t \sin(t) ) and ( y(t) = t \cos(t) - t \sin^2(t) ) with respect to ( t ), you will use the chain rule and product rule where necessary.

[ \frac{dx}{dt} = e^t \sin(t) + e^t \cos(t) ] [ \frac{dy}{dt} = \cos(t) - t \sin(t) - 2t \cos(t) \sin(t) ]

These are the derivatives of ( x(t) ) and ( y(t) ) with respect to ( 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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