Differentiate $f(x)=\ln \left(7 x^{2}-17\right)$ \[ f^{\prime}(x)= \]

Step 1 ：Given the function \(f(x)=\ln(7x^{2}-17)\)

Step 2 ：We need to find the derivative of this function.

Step 3 ：We can use the chain rule for differentiation, which states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Step 4 ：In this case, the outer function is \(\ln(x)\) and the inner function is \(7x^{2}-17\).

Step 5 ：The derivative of \(\ln(x)\) is \(1/x\) and the derivative of \(7x^{2}-17\) is \(14x\).

Step 6 ：Therefore, the derivative of the function \(f(x)\) is \(f'(x) = \frac{1}{7x^{2}-17} * 14x\).

Step 7 ：Simplifying this expression, we get \(f'(x) = \frac{14x}{7x^{2}-17}\).

Step 8 ：\(\boxed{f'(x) = \frac{14x}{7x^{2}-17}}\) is the final answer.