derivative of f(x) = x/(sqrt(x^2-4))

Answer 1

I would rewrite it as
y = x(x^2 - 4)^(-1/2_
then use the product rule

dy/dx = x(-1/2)(x^2-4)^(-3/2)(2x) + (x^2-4)^(-1/2)
we could factor that

dy/dx = (x^2-4)^(-3/2)[-x^2 + x^2-4]

= -4/(x^2-4)^(3/2)

check my work, I did not write it on paper first, did all the steps as I typed.