y = (tan x)^(1/x), Using the Log Rule

You'll have to use the Log rule find the derivative of y=(tan x)^(1/x). I wrote a very long explanation on exactly how to do this, and if you're interested in reading it, I've included a link so you can down load the word document.

The image I've included in this post gives you the basic steps for finding the derivative, with out any explanation. So if you're up to speed on taking simple derivatives you should be able to follow the picture from one line to the next.

Anyway couple of interesting things about this function. One is since it involves the tan function, it is undefined at the half pi's. Two is that it's derivative has a natural log function in it so it is undefined for all x <= 0.

Overall it's a strange function I'd say.

If you really want to get into the nitty gritty down load the word doc.
LogRuleExplanation.doc