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I have black-box access to some function and I want to compute the derivative about the point X. Is there a method that does this?

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    $\begingroup$ en.wikipedia.org/wiki/Numerical_differentiation. Or did you have a more specific question? $\endgroup$ – Dave Kielpinski Oct 18 '17 at 23:13
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    $\begingroup$ @DaveKielpinski No this was it. There's at least one notion of a "simplex gradient" that was introduced for this reason: this inspires me to look further. $\endgroup$ – 彼得名姓 Oct 19 '17 at 12:22
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http://en.wikipedia.org/wiki/Numerical_differentiation

Or did you have a more specific question?

(posted following @gung's encouragement above)

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  • $\begingroup$ Thank you for pointing in the right direction. I think Wikipedia skirts around the issue, though: the key is to compute the derivative while obtaining an error estimate for the answer. It doesn't seem to address that issue at all. $\endgroup$ – whuber Sep 5 '18 at 17:54
  • $\begingroup$ Error estimates for derivatives are not mentioned in the question. If you want to create a new question around that, I can try to answer. Upvoting my current answer would be encouraging in that regard :) $\endgroup$ – Dave Kielpinski Sep 6 '18 at 18:30
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    $\begingroup$ Although error estimates were not mentioned in the question, I was trying to put forward the view that any discussion of numerical differentiation in such a context (a "black box") on this site (which concerns statistical analysis) needs to acknowledge the possibility of making such estimates and the importance of doing so. Indeed, whenever the answer to a question here on CV is a single line, that's a sign the answer is incomplete and perhaps ought to be expanded (or perhaps the question ought to be closed as unsuitable for our format). $\endgroup$ – whuber Sep 6 '18 at 19:38
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    $\begingroup$ That's an interesting point of view. You're obviously one of the people who runs things around here, so do what you like, but I wouldn't have assumed that. I just try to answer the questions as they're posed, and the OP was satisfied. 🤷 $\endgroup$ – Dave Kielpinski Sep 6 '18 at 23:00

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