Final answer:
To find the derivative of f(x) = arcsin(x-3), use the chain rule. The derivative is 1/sqrt(1-(x-3)^2).
Step-by-step explanation:
To find the derivative of the function f(x) = arcsin(x-3), we can use the chain rule. The chain rule states that if we have a function g(x) = h(u(x)), then the derivative of g(x) with respect to x is equal to the derivative of h(u(x)) with respect to u multiplied by the derivative of u(x) with respect to x.
In this case, h(u) = arcsin(u) and u(x) = x-3. Taking the derivative of h(u) with respect to u gives us 1/sqrt(1-u^2) and the derivative of u(x) with respect to x is 1.
Therefore, the derivative of f(x) = arcsin(x-3) is (1/sqrt(1-(x-3)^2)) * 1 = 1/sqrt(1-(x-3)^2).