Find the derivative of the function y = f(x) =
(xsquared + 1) divided by (x squared - 1) all raised to the 3rd power

3

Question

Find the derivative of the function y = f(x) =
(xsquared + 1) divided by (x squared - 1) all raised to the 3rd power

3

anonymous · Answer

You're going to use the chain rule and then the quotient rule here. If you give me a minute I can work it out for you.

anonymous · Answer

you could also distribute the power to top and bottom quantities, change the second one to a negative power, then just use the product rule and power rule.

anonymous · Answer

i dont know where to start since the whole thing is raised to 3. do i get rid of that first?

anonymous · Answer

have you learned the chain rule yet?

anonymous · Answer

yes.

anonymous · Answer

Well, think of that big fat (x^2+1)/(x^2-1) as one quantity. Dealing with it is no different than dealing with x^3, except you have the chain rule afterwards.

anonymous · Answer

so you get 3(bigfatmess)^2(dbigfatmess)

anonymous · Answer

when doing the quotient rule, do you do derivative of top first - derivative of bottom or does it matter.

anonymous · Answer

did you learn low-dee-high minus high-dee-low over low low? That helps me remember.

The order on top matters because of the negative. (really, you can switch them as long as you keep the signs straight)