Question

Differentiate f. f(x) = x / (1 - ln(x - 3))

Answer 1

And find the domain of f.

Answer 2

f'(x)= [1 - ln(x - 3)] - x[-(1/x-3)]/[1 - ln(x - 3)] ^2

Answer 3

f'(x)= [1 - ln(x - 3)] + (x/x-3)/[1 - ln(x - 3)] ^2

Answer 4

f'(x) = 1/[1 - ln(x - 3)] + (x/x-3)/[1 - ln(x - 3)] ^2

Answer 5

The domain is where the denominator is not zero, otherwise its undefined\[1-\ln(x-3)=0\rightarrow 1=\ln(x-3)\rightarrow e=x-3\rightarrow e+3=x\]
so \[x >e+3\]

Answer 6

\[x/((x-3)(1-ln (x-3))^2)+1/(1-ln(x-3))\]