Differentia te f and find the domain of f. (Enter the domain in interval notation.) f(x) = x/ 1 − ln(x − 2)

Answer 1

f(x) = x/(1-ln(x-2))

Use quotient rule

f '(x) = (1(1-ln(x-2)) - x(-1/(x-2)))/(1-ln(x-2))²

= (1-ln(x-2) +x/(x-2))/(1-ln(x-2))²

Domain of f(x). Two constraints:

1-ln(x-2) ≠ 0 and x-2 > 0 because ln(z) for z<=0 is undefined. So x>2.

x-2 ≠ e because ln(e) = 1, which will cause a zero in the denominator.

x ≠ e+2

Domain of f(x): (2, e+2) U (e+2, ∞)