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

Domain cannot have x²=1, Domain is (-∞,-1)U(-1,1)U(1,∞)

|1-x²|=1-x² when x²<1,,,x<1 and x>-1

|1-x²|=x²-1 when x²>1 ,,x>1 and x<-1

function 1

f(x)=ln(1-x²)^1/2 ,,, for x domain (-1,1)

f'(x)=(1-x²)^-1/2[(1/2)(1-x²)^-1/2(-2x)=(-)x/(1-x²)

fuction 2 ,,, for x domain (-∞,-1)U(1,∞)

f(x)=ln(x²-1)^1/2

f'(x)=(x²-1)^-1/2[(1/2)(x²-1)^-1/2(2x)=x(x²-1)

Answer 2

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