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

Now, by the Rule for Parametric Differentiation,

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To differentiate the parametric equations (x(t) = -t - e^t) and (y(t) = -2t^2 - 2t^3e^t), you would differentiate each equation separately with respect to (t), using the chain rule when necessary.

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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.

- For #f(t)= (sin^2t,cos^2t)# what is the distance between #f(pi/4)# and #f(pi)#?
- What is the arclength of #f(t) = (cos2t-sin2t,tan^2t)# on #t in [pi/12,(5pi)/12]#?
- What is the arclength of #f(t) = (sin^2t-cos2t,t/pi)# on #t in [-pi/4,pi/4]#?
- What is the slope of #f(t) = (t^2+2t,2t-3)# at #t =-1#?
- What is the derivative of #f(t) = (e^(t^2-1)+3t, -t^3+t ) #?

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