Find the derivative of the function. \[ g(x)=9 \arccos \left(\frac{x}{6}\right) \] \( g^{\prime}(x)=\square \)

We are given the function   g(x) = 9 · arccos(x/6). Step 1. Recall that the derivative of arccos(u) with respect to x is   d/dx [arccos(u)] = –u' / √(1 – u²). Step 2. Here, u = x/6 so that u' = 1/6. Step 3. Differentiate using the chain rule:   g'(x) = 9 · d/dx [arccos(x/6)]      = 9 · [ –(1/6) / √(1 – (x/6)²) ]      = –9/(6√(1 – (x/6)²)). Step 4. Simplify the constant:   –9/(6√(1 – (x/6)²)) = –3/(2√(1 – (x/6)²)). Thus, the derivative is:   g'(x) = –3/(2√(1 – (x/6)²)). Alternatively, since √(1 – (x/6)²) = √((36 – x²)/36) = √(36 – x²)/6, you can also write:   g'(x) = –3/(2 · (√(36 – x²)/6)) = –9/√(36 – x²). Both forms are equivalent.