Find f''(1/2) using f(x) = ln(1-x).
f'(x) = 1/(1-x) * -1 = -1/(1-x)
so then using quotient rule:
f''(x) = ((-1*-1) - ((1-x)(0))) / (1-x)^2
f''(1/2) = 1/(1-(1/2))^(2) = 4
Is this correct?
I would have taken the first derivative of -1/(1-x) and simplified it to
1/(x-1) or (x-1)^-1
(If my numerator or my denominator is a constant, I seldom use the quotient rule, since one part drops out anyway)
y' = (x-1)^-1
y'' = -1(x-1)^-2
= -1(x-1)^2
f '' (1/2) = -1/(1/2 - 1)^2
= -1/(1/4) = -4
in your quotient rule, it looks like you "reversed" the two products,
if y = u/v
then y' = (vu' - uv')/v^2 , you have it "backwards"
A very common mistake, which is avoided using my approach.