I wanted to differentiate (cos(x))^x(adsbygoogle = window.adsbygoogle || []).push({});

Applying the chain rule I got -x(sinx)(cosx)^(x-1)

But when I go to WolframAlpha, they show

d/dx(cos^x(x)) = cos^x(x) (log(cos(x))-x tan(x))

Why the extra term? Why doesn't the simple chain rule apply?

I have got strange results from WolframAlpha before

eg try typing (-1)^(1/3)

You don't get -1 as a root.

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# Puzzled by WolframAlpha

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