Differentiate Archimedes's spiral I read that the only problem of differential calculus Archimedes solved was constructing the tangent to his spiral,
$$r = a + b\theta$$
I would like to differentiate it but I don't know much about differentiating polar functions and can't find this particular problem online. Without giving me a full course in differential geometry, how does one calculate the tangent to the curve at $\theta$?

You can parametrize it in the cartesian plane as
$$s(t)=\begin{pmatrix}bt\cos(t-a/b)\\bt\sin(t-a/b)\end{pmatrix}$$
So the direction of the tangent line at a point $s(t)$ is given by
$$s'(t)=\begin{pmatrix}b\cos(t-a/b)-bt\sin(t-a/b)\\b\sin(t-a/b)+bt\cos(t-a/b)\end{pmatrix}$$
