True or false: If $f(x)=\ln (x)$, then \[ f^{\prime \prime}(x)=-\frac{1}{x^{2}} \] True False

Step 1 ：Given the function \(f(x)=\ln (x)\), we are asked to verify if the second derivative of the function is \(-\frac{1}{x^{2}}\).

Step 2 ：First, we find the first derivative of \(f(x)\), which is \(f'(x) = \frac{1}{x}\).

Step 3 ：Next, we find the second derivative of \(f(x)\), which is \(f''(x) = -\frac{1}{x^{2}}\).

Step 4 ：Comparing this with the given second derivative, we see that they are the same.

Step 5 ：Final Answer: The second derivative of \(f(x)=\ln (x)\) is indeed \(-\frac{1}{x^{2}}\). Therefore, the statement is \(\boxed{\text{True}}\).