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How do you differentiate the following parametric equation: # x(t)=-te^t+t, y(t)= 3t^3-4t #?

Answer 1

Emma Aldridge

#frac{dy}{dx} = frac{9t^2 - 4}{1 - (t + 1)e^t}#

#frac{dx}{dt} = 1 - (t + 1)e^t#

#frac{dy}{dt} = 9t^2 - 4#

Using the Chain Rule,

#frac{dy}{dx} = frac{ frac{dy}{dt} }{ frac{dx}{dt} }#

#= frac{9t^2 - 4}{1 - (t + 1)e^t}#

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Answer 2

Samantha Adkison

To differentiate the parametric equations (x(t) = -te^t + t) and (y(t) = 3t^3 - 4t), compute the derivatives of (x(t)) and (y(t)) with respect to (t). The derivatives are as follows:

[ \frac{dx}{dt} = -e^t - te^t + 1 ]

[ \frac{dy}{dt} = 9t^2 - 4 ]

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Answer from HIX Tutor

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.