Help with Practice Quiz? :)

[OhhCalculus]

So, I wish I had a clue what I was doing, but I don't. So, don't get angry if since I can't provide any of my own work. I've been absent and therefore don't really have a clue what we're doing in class. We have a quiz tomorrow and were provided a practice quiz today. It's two problems, I need help with one of them.

We're given...
y = fourth square root of : x^2 +1/x^2-1

and we're expected to find y'

If you don't wanna work all of it out (which would be helpful), at least giving me the first step would also be beneficial. Thanks.

 

[mmm4444bot]

The statement "I don't have a clue" is meaningless, to me.

If you don't understand that the notation y` means the first derivative of y, then you're toast.

If you do understand this notation, then you do have at least one clue.

Here's some steps for one possible approach.

Switch the fourth-root notation to exponential notation. (By the way, it's called a fourth root, not a fourth square root.)

\(\displaystyle y = \left (\frac{x^2 + 1}{x^2 - 1} \right )^{1/4}\)

If you've learned the product rule for finding the derivative of a product, you could continue by factoring the expression on the right above into a product.

\(\displaystyle (x^2 + 1)^{1/4} \cdot (x^2 - 1)^{-1/4}\)

Don't forget to apply the chain rule, while working out the product rule, since each of the two factors is a composite function of x.

If you have not yet learned the product and chain rules, then you're not ready to prepare for your quiz tomorrow. We cannot teach over the Internet all of the information that you missed while absent.