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# What to return for non-differentiable points
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!!! info "What is the short version?"
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If the function is not differentiable due to e.g. a branch, like `abs`, your rule can reasonably claim the derivative at that point is the value from either branch, *or* any value in-between (e.g. for `abs` claiming 0 is a good idea).
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If it is not differentiable due to the primal not being defined on one side, you can set it to what ever you like.
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Your rule should claim a derivative that is *useful*.
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In calculus one learns that if the derivative as computed by approaching from the left,
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and the derivative one computes as approaching from the right are not equal then the derivative is not defined,
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and we say the function is not differentiable at that point.
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