Does anyone outside there know of a package helping to plot the tangent to a 2d curve (not being a circle) at a given point?
In Maple 8 you could compute the tangent line using the procedure TangentLine in the new VectorCalculus package.
Otherwise, just compute it yourself: if it’s a parametric curve x = X(t), y = Y(t), the tangent line at t=t0 is parametrically
x = X(t0) + D(X)(t0)*s, y = Y(t0) + D(Y)(t0)*s
Or if the curve is given implicitly by F(x,y) = c and [x0,y0] is a point on the curve where the gradient of F is nonzero, the tangent line is given implicitly by
(x-x0)*D(F)(x0,y0) + (y-y0)*D(F)(x0,y0) = 0
or parametrically by
x = x0 + s*D(F)(x0,y0), y = y0 - s*D(F)(x0,y0)