Proof of polar $\frac{d y}{d x}$ $dy/dx$ ?

Question

i.e. $dy/dx=\doty/\dotx=(r'\sin\theta+r\cos\theta)/(r'\cos\theta-r\sin\theta)$

My assumption is that it's the product rule, given that $y=r\sin\theta$ and $x=r\cos\theta$

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Answer 1 · 2018-05-25T01:55:34

See proof below

$\doty=d/(d\theta)(r\sin\theta)=r'\sin\theta+r\cos\theta$

$\dotx=d/(d\theta)(r\cos\theta)=r'\cos\theta+r(-\sin\theta)$