Final answer:
To find the derivative of the given function, we can use the power rule for differentiation.
Step-by-step explanation:
To find the derivative of the function y = (1/2)x^8 - (1/3)x^3, we can use the power rule for differentiation. The power rule states that the derivative of xn is nx^(n-1). Applying this rule, we can differentiate each term separately:
The derivative of (1/2)x^8 is (8/2)x^(8-1) = 4x^7.
The derivative of (1/3)x^3 is (3/3)x^(3-1) = x^2.
Therefore, the derivative of y = (1/2)x^8 - (1/3)x^3 is dy/dx = 4x^7 - x^2.