[Docs] [AutoDiff] Add default derivative subsection and fix minor issues.

[rxwei]

• Add section "Default derivatives", which documents what's discussed here.
• .withoutDerivative() -> withoutDerivative(at:)
• Fix syntax error in default derivatives.

[dan-zheng]

LGTM! Though I'd recommend waiting for @marcrasi to review also.

[marcrasi]

Looks like a good solution to me.

I have one question. What happens if a user defines a @derivative of a @differentiable(default) method?

[dan-zheng]

I have one question. What happens if a user defines a @derivative of a @differentiable(default) method?

It seems to me that should be rejected: @derivative and @differentiable(default) are in conflict.

[rxwei]

Looks like a good solution to me.

I have one question. What happens if a user defines a @derivative of a @differentiable(default) method?

I think this should be banned if it’s in the same module. Cross module should be allowed for flexibility, but can be banned in the initial proposal.

[rxwei]

@swift-ci please smoke test and merge

[bartchr808]

This:

I have one question. What happens if a user defines a @Derivative of a @differentiable(default) method?

Made me think about whether there would be any problems with dynamic lookup of functions, but as far as I can tell there aren't any weird cases.

[rxwei]

That should be orthogonal, as statically the only thing involved is subscript(dynamicMember:). Derivative registration only cares about member declarations in terms of static lookup.