Final answer:
To find dy/dx, apply the chain rule and product rule to differentiate the function involving a square root and inverse sine, then simplify the result.
Step-by-step explanation:
To find dy/dx of the given function y = x√(a² - x²/2 + a²/2sin⁻¹(x/a)), we need to use the chain rule and product rule for differentiation. By applying these rules, we can compute the derivative step by step, keeping in mind the derivatives of basic functions such as the square root, trigonometric functions, and their inverses. Unfortunately, without a clearer expression, the specific application of the differentiation rules to this function cannot be outlined in detail. However, once the derivative is calculated, simplification may involve combining like terms and simplifying expressions involving the constant a.