For a curve given in polar form by

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

For a curve given in polar form by r=f(θ)r=f(\theta), let r′=drdθr'=\dfrac{dr}{d\theta}. Which of the following expressions is equal to dydx\dfrac{dy}{dx} for the curve? (a) r′cos⁡θ−rsin⁡θ r′sin⁡θ+rcos⁡θ \dfrac{r'\cos\theta-r\sin\theta}{\,r'\sin\theta+r\cos\theta\,} (b) r′cos⁡θ+rsin⁡θ r′sin⁡θ−rcos⁡θ \dfrac{r'\cos\theta+r\sin\theta}{\,r'\sin\theta-r\cos\theta\,} (c) r′sin⁡θ+rcos⁡θ r′cos⁡θ−rsin⁡θ \dfrac{r'\sin\theta+r\cos\theta}{\,r'\cos\theta-r\sin\theta\,} (d) r′sin⁡θ+rcos⁡θ r′cos⁡θ+rsin⁡θ \dfrac{r'\sin\theta+r\cos\theta}{\,r'\cos\theta+r\sin\theta\,}

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