Home | 18.022 | Chapter 3 | Section 3.1

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(x + y)-1 is not differentiable  and  singular on the line (or plane, in three dimensions) x = -y, and differentiable everywhere else.

The angle tan-1(y / x) which will be called here, is differentiable everywhere but at the origin, r = 0, where it is not even continuous.

In three dimensions, r = 0 defines a straight line.