"Differentiate y= square root(x^2 1) from fist principles." I have no idea where to begin. Please help!

Some of your math symbols didn't come through. I assume you mean this:



I won't solve this for you, but will give you another example that illustrates the process. You can then apply the process to your problem.

Suppose you want to differentiate



You can start by substituting a new function g(x) for the part inside the parentheses:



Now apply the chain rule:



Hope this helps.

Yes, sorry, my symbols didn't really come through quite as I expected. I do understand how to differentiate a problem using the chain rule, which I assume is what you used in your example; however I am having trouble doing the same thing from first principles (you know, this one: http://intmstat.com/differentiation/Image536.gif) Thank you for helping though. By the way, you were right about your assumption of what I meant.

The definition of the derivative is:



Using the chain rule:


So let's take a look at the example I gave earlier. We can set:

and


Now we find the derivatives of these two functions from first principals.



and:


Then apply the chain rule:



You can use this same process on your problem, setting and . Give it a try and post back with what you get.

Hope this helps.