Find the derivative of the function. \[ y=\ln \left(4 x^{3}-x^{2}\right) \] A. $\frac{4 x-2}{4 x^{2}-x}$ B. $\frac{12 x-2}{4 x^{2}}$ c. $\frac{12 x-2}{4 x^{3}-x}$ D. $\frac{12 x-2}{4 x^{2}-x}$

Step 1 ：Given the function \(y = \ln(4x^3 - x^2)\), we are asked to find its derivative.

Step 2 ：We can use the chain rule to find the derivative of this function. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Step 3 ：In this case, the outer function is the natural logarithm and the inner function is \(4x^3 - x^2\).

Step 4 ：The derivative of the natural logarithm of a function \(f(x)\) is \(\frac{1}{f(x)}\), and the derivative of \(4x^3 - x^2\) is \(12x^2 - 2x\).

Step 5 ：So, the derivative of the function \(y = \ln(4x^3 - x^2)\) is \(\frac{1}{4x^3 - x^2} \times (12x^2 - 2x)\), which simplifies to \(\frac{12x^2 - 2x}{4x^3 - x^2}\).

Step 6 ：Final Answer: The derivative of the function \(y = \ln(4x^3 - x^2)\) is \(\boxed{\frac{12x^2 - 2x}{4x^3 - x^2}}\). This corresponds to option D.