Mr. Integral
Math notes/Calculus II/Parametric and Polar Calculus

Parametric Curves and Motion — Cheat sheet

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Core rule

dydx=y′x′,d2ydx2=(y′/x′)′x′,L=∫x′2+y′2 dt.\frac{dy}{dx}=\frac{y'}{x'},\quad \frac{d^2y}{dx^2}=\frac{(y'/x')'}{x'},\quad L=\int\sqrt{x'^2+y'^2}\,dt.

Watch for

Slope formulas require x′≠0x'\ne0. Distance counts repeated traversal, while displacement depends only on endpoints.