# Calc10_1 - 10.1 Parametric Functions 6 4 2-6-4-2 0-2-4-6 2...

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10.1 Parametric Functions Greg Kelly, Hanford High School, Richland, Washington

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In chapter 1, we talked about parametric equations. Parametric equations can be used to describe motion that is not a function. ( 29 ( 29 x f t y g t = = If f and g have derivatives at t , then the parametrized curve also has a derivative at t .
The formula for finding the slope of a parametrized curve is: dy dy dt dx dx dt = This makes sense if we think about canceling dt .

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The formula for finding the slope of a parametrized curve is: dy dy dt dx dx dt = We assume that the denominator is not zero.
To find the second derivative of a parametrized curve, we find the derivative of the first derivative: dy dt dx dt = 2 2 d y dx ( 29 d y dx = 1. Find the first derivative ( dy/dx ). 2. Find the derivative of dy/dx with respect to t . 3. Divide by dx/dt .

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Example 2 (page 514): 2 2 3 2 Find as a function of if and . d y t x t t y t t dx = - = -
Example 2 (page 514): 2 2 3 2 Find as a function of if and .

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