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

The derivative of the parametric equation is

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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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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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- How do you find the equations of the tangents to that curve #x=3t^2 + 1# and #y=2t^3 + 1# that pass through point (4,3)?
- What is the derivative of #f(t) = (t^2+1 , e^(2t^2-2) ) #?

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