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How do you find derivatives of parametric functions?

Answer 1

Emma Aldridge

For the parametric equations

#{(x=x(t)),(y=y(t)):}#,

we can find the derivative

#{dy}/{dx}={{dy}/{dt}}/{{dx}/{dt}}={y'(t)}/{x'(t)}#.

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Answer 2

Emilia Aguilar

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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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.