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

Answer 1

Scarlett Allison

#dy/dx=(3e^(3t))/(2t-e^t-te^t)#

#x'(t)=2t-e^t-te^t# #y'(t)=3e^(3t)#

The derivative of the parametric equation is

#dy/dx=(y'(t))/(x'(t))=(3e^(3t))/(2t-e^t-te^t)#

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Answer 2

Evelyn Agard

To differentiate the given parametric equations (x(t) = t^2 - te^t) and (y(t) = e^{3t}), follow these steps:

Differentiate (x(t)) with respect to (t) to find (dx/dt).
Differentiate (y(t)) with respect to (t) to find (dy/dt).
The derivatives (dx/dt) and (dy/dt) represent the rates of change of (x) and (y) with respect to (t), respectively.

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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.