Find $\frac{d y}{d x}$ for the following function. \[ y=\frac{3 \cos x}{6-7 \cos x} \]

Step 1 ：Given the function \(y=\frac{3 \cos x}{6-7 \cos x}\), we are asked to find its derivative \(\frac{d y}{d x}\).

Step 2 ：We will use the quotient rule for differentiation, which states that the derivative of a quotient u/v is \(\frac{vu' - uv'}{v^2}\), where u' and v' are the derivatives of u and v respectively.

Step 3 ：Let's identify u and v in our function. We have u = 3cosx and v = 6 - 7cosx.

Step 4 ：Next, we find the derivatives of u and v. The derivative of u, denoted as du, is -3sinx. The derivative of v, denoted as dv, is 7sinx.

Step 5 ：We substitute these values into the quotient rule formula to find the derivative of the function. This gives us \(\frac{d y}{d x} = \frac{-3*(6 - 7\cos(x))*\sin(x) - 21*\sin(x)*\cos(x)}{(6 - 7\cos(x))^2}\).

Step 6 ：\(\boxed{\frac{d y}{d x} = \frac{-3*(6 - 7\cos(x))*\sin(x) - 21*\sin(x)*\cos(x)}{(6 - 7\cos(x))^2}}\) is the final answer.