# How do you find derivatives of parametric functions?

For the parametric equations

we can find the derivative

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To find the derivatives of parametric functions, use the chain rule and differentiate each parametric equation separately with respect to the parameter. For example, if the parametric equations are ( x = f(t) ) and ( y = g(t) ), then the derivatives are given by ( \frac{dx}{dt} = \frac{df}{dt} ) and ( \frac{dy}{dt} = \frac{dg}{dt} ).

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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.

- What is the derivative of #f(t) = (tlnt, 3t^2-t ) #?
- What is the arc length of the curve given by #r(t)= (1/t,1,t)# on # t in [0, 1]#?
- What is the arc length of the curve given by #r(t)= (9sqrt(2),e^(9t),e^(-9t))# on # t in [3,4]#?
- How do you differentiate the following parametric equation: # (t-t^3,3/t^4-t^3)#?
- A soccer ball kicked at the goal travels in a path given by the parametric equations: x=50t; #y=-16t^2+32t#, At what two times will the ball be at a height of 6ft.?

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