Hello, I am looking at some notes and cannot understand the following example:(adsbygoogle = window.adsbygoogle || []).push({});

Suppose x^{2}+ y^{2}= a^{2}

Note: (Optional) use the equation of the curve to convert all vector components to the same differential, e.g.

[tex]\frac{dy}{dx} = \frac{1}{2}\frac{-4x}{\sqrt{a^2-x^2}} \Rightarrow dy = \frac{-2x}{y}dx \Rightarrow \vec{dl} = dx\hat{x} - \frac{2x}{y}dx\hat{y}[/tex]

Question: I don't understand the second arrow which leads to the following conclusion:

[tex]\vec{dl} = dx\hat{x} - \frac{2x}{y}dx\hat{y}[/tex]

Why wouldn't there be a dy?

Thanks,

JL

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# How to Define Differential Length Vectors

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