Find the derivative of the function. \[ f(x)=\arcsin (x-2) \] \( f^{\prime}(x)=\square \)

To find the derivative of the function \( f(x) = \arcsin(x - 2) \), we can use the chain rule. The derivative of \( \arcsin(u) \) is \( \frac{1}{\sqrt{1 - u^2}} \), where \( u = x - 2 \). Thus, we have: 1. First, we find \( u' = 1 \) since the derivative of \( u = x - 2 \) with respect to \( x \) is simply 1. 2. Therefore, the derivative \( f'(x) \) is given by: \[ f'(x) = \frac{1}{\sqrt{1 - (x - 2)^2}} \cdot 1 = \frac{1}{\sqrt{1 - (x - 2)^2}} \] So, \[ f'(x) = \frac{1}{\sqrt{1 - (x - 2)^2}} \] is the final answer! Be cautious with the domain of arcsin to ensure \( -1 \leq x - 2 \leq 1 \).