Answer
$$
f(x)=\ln \left(x^{2}-2 x\right)
$$
Differentiating both sides of this equation we have
$$
\begin{aligned}
f^{\prime}(x)&=\frac{1}{x^{2}-2 x}(2 x-2)\\
&=\frac{2(x-1)}{x(x-2)}
\end{aligned}
$$
Domain of f is given by:
$$
\operatorname{Dom}(f)=\{x \mid x(x-2)>0\}=(-\infty, 0) \cup(2, \infty).
$$
Work Step by Step
$$
f(x)=\ln \left(x^{2}-2 x\right)
$$
Differentiating both sides of this equation we have
$$
\begin{aligned}
f^{\prime}(x)&=\frac{1}{x^{2}-2 x}(2 x-2)\\
&=\frac{2(x-1)}{x(x-2)}
\end{aligned}
$$
Domain of f is given by:
$$
\operatorname{Dom}(f)=\{x \mid x(x-2)>0\}=(-\infty, 0) \cup(2, \infty).
$$
