Final answer:
To find y³, substitute the function y into the equation and raise it to the power of 3. To find y', differentiate the function y with respect to x using the product rule.
Step-by-step explanation:
To find y³ for the function y = x√(64 - x^2), we substitute the function y into the equation and raise it to the power of 3. This gives us (x√(64 - x^2))³. To find y', we differentiate the function y with respect to x using the product rule. The derivative of y is given by y' = (√(64 - x^2)) + (x*(-2x)/(2√(64 - x^2))) = (√(64 - x^2)) - (x^2/√(64 - x^2)).