`y=cos^(-1)((3cosx-4sinx)/(5))`, then `(dy)/(dx)=`

Explanation

To find the derivative of the function \( y = \cos^{-1}\left(\frac{3\cos x - 4\sin x}{5}\right) \), we will follow these steps:

### Step 1: Differentiate using the chain rule
We know that the derivative of \( \cos^{-1}(u) \) is given by:
\[ \frac{dy}{dx} = -\frac{1}{\sqrt{1 - u^2}} \cdot \frac{du}{dx} \]
where \( u = \frac{3\cos x - 4\sin x}{5} \).
...