calculus Help!!!

Question

Consider the function defined by f(x)= ln( sqrt(|1−x^2|)). •

a) State the domain of this function.

b) Determine the derivative of ln(sqrt(|1−x^2|)).Be careful to show your work.

Answer 1

f(x_ = ln(√I(1 - x²))

a)1 - x² ≠ 0; x ≠ ±1

Domain: (- ∞, - 1)U(-1 , 1)u(1, ∞)

b) If - 1 < x < 1, then lf(x) = ln(√I1 - x²I)) = 1/2ln(1 - x²); f'(x) = 1/2·1/(1 - x²)·(- 2x) = x/(x² - 1)

If x from (- ∞, - 1)U(1, ∞) then f(x) = 1/2ln(x² - 1); f'(x) = 1/2·1/(x² - 1)·2x = x//(x² - 1)

Answer: f'(x) = x/(x² - 1)