can someone help me on the attachment and not go to wolfframealpha to show me how to work it

Question

anonymous · Answer

attachment

turingtest · Answer

$$f(x)=(x^2-2)/\sqrt{x^2-1}$$
quotient rule would be a pain here so let's rewrite this as a product of two functions:
$$f(x)=(x^2-2)/\sqrt{x^2-1}=(x^2-2)(x^2-1)^(-1/2)$$
that's (x^2-1)^(-1/2) on the right there...
product rule (fg)'=f'g+g'f

anonymous · Answer

ok

turingtest · Answer

$$f'(x)=2x(x^2-1)^(-1/2)-(x^2-2)(1/2)(x^2-1)^(-3/2)(2x)$$
$$=2x/\sqrt{x^2-1}-(x^3-2x)/\sqrt{(x^2-1)^3}$$
simplify

anonymous · Answer

but that not one of the answer choices here a list

anonymous · Answer

the first answer choice is on the first attachment where its show the problem