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Tangent Lines The Derivative of Parametric Equations

equation!Sal finds the second derivative of the function defined by the parametric equations x=3eยฒแต and y=3ยณแต-1. If you're seeing this message, it means we're having trouble loading external resources on our website.

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The second derivative is, by definition, \frac {d^2y} {dx^2} = \frac {d} {dx} \frac {dy} {dx}. dx2d2y = dxd dxdy. By the chain rule, \frac {d} {dx} = \frac {d} {dt} \frac {1} {\hspace {1mm} \frac {dx}

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Definition: Second Derivative of a Parametric Equation. Let ๐ and ๐ be differentiable functions such that ๐ฅ and ๐ฆ are a pair of parametric equations: ๐ฅ = ๐ ( ๐ก), ๐ฆ = ๐ ( ๐ก). Then, we can define the second

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Our next goal is to see how to take the second derivative of a function defined parametrically. The second derivative of a function y = f(x) is defined to be the derivative of the

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