Feynman’s Tips on Physics describes the following trick to take derivatives quickly.

Suppose

is a function mapping reals to reals.

Then

Next notice that each of these terms *almost* has itself in it, so we factor out.

.

That’s the trick. It’s not incredibly powerful, but here’s how it works on an example:

.

We’ll let

Next we write over again.

.

Then insert .

And then add .

.

Finish it up with .

.

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Tags: differentiation

This entry was posted on May 10, 2009 at 4:25 pm and is filed under math. You can follow any responses to this entry through the RSS 2.0 feed.
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May 11, 2009 at 6:32 am

Nice Tip. Thanks!

February 11, 2014 at 2:12 pm

This is a fun one. You can also derive the general formula using logarithmic differentiation, which is a little faster.