Differentiate $f(x)=\ln \left(7 x^{2}-17\right)$
\[
f^{\prime}(x)=
\]
\(\boxed{f'(x) = \frac{14x}{7x^{2}-17}}\) is the final answer.
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.