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How do you differentiate the following parametric equation: # x(t)=-3e^t-2t, y(t)= -5t^2-e^(4t) #?

Answer 1

Evelyn Agard

#dy/dx=(10t+4 e^(4t))/(3 e^t +2)#

Solve #dy/dt# and #dx/dt#

after which divide #dy/dt# by #dx/dt# to obtain #dy/dx#

#dy/dx=(dy/dt)/(dx/dt)#

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Answer 2

Aurora Alvarado

To differentiate the given parametric equations ( x(t) = -3e^t - 2t ) and ( y(t) = -5t^2 - e^{4t} ):

Differentiate each equation with respect to ( t ) separately.

( \frac{dx}{dt} = \frac{d}{dt}(-3e^t - 2t) = -3e^t - 2 )

( \frac{dy}{dt} = \frac{d}{dt}(-5t^2 - e^{4t}) = -10t - 4e^{4t} )

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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.