Calculus/Polar Differentiation

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Differential calculus[edit]

We have the following formulae:

To find the Cartesian slope of the tangent line to a polar curve r(θ) at any given point, the curve is first expressed as a system of parametric equations.

Differentiating both equations with respect to θ yields

Dividing the second equation by the first yields the Cartesian slope of the tangent line to the curve at the point (rr(θ)):