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

Simple Projectile Motion

Ever get one of those problems.. that sounds something like..
"Roy hits a baseball at an angle of 30 degrees with respect to the horizontal at a velocity of 30 mph.
a. determine how high the baseball will go
b. determine how far the baseball will go"
and so on and so forth.
Well I've explained just about everything I know about simple projectile motion in this animated excel spread sheet. Including a nice little explanation of the calculus behind the equations of motion.
SimpleProjectileMotion.xls

Water Trough Practical Application

A 10ft long trough whose sides are shaped like isosceles triangles with a height of 1ft and a base of 3ft, fills up with water at a rate of 12 cubic feet per minute. How fast is the water rising when the water is 6 inches deep?

I created an excel spread sheet that illustrates whats going on here very nicely. But I'll leave one hint right here. The key is to write an equation that relates the depth of the water to the volume of the water. Follow the link to download the xls file.

WaterTroughProblem.xls

x^2y^2 + xsiny = 4, Implicit Differentiation

x^2y^2 + xsiny = 4
This problem requires you to use implicit differentiation in conjunction with the product rule and the chain rule. The thing that might scare you about this problem is the xsiny part but don't worry

x^2 + xy - y^2, Implicit Differentiation

This problem requires implicit differentiation because the equation cannot be solved for y. The fun part about this problem is that you get to use the product rule on the xy term in the middle of the equation.

Click on the image below to see a lager version of my solution.