Answer :
Final answer:
The derivative of the function f(x) = x^(2/3) - 4x^9 - 11x, denoted as f'(x), is found by applying the power rule and is f'(x) = (2/3)*x^(-1/3) - 36x^8 - 11.
Explanation:
The student is asking for the derivative of the function f(x) = x^(2/3) - 4x^9 - 11x. To find f'(x), we need to apply the power rule for derivatives, which says that the derivative of x^n with respect to x is n*x^(n-1). Applying the power rule to each term in the function:
• The derivative of x^(2/3) is (2/3)*x^(-1/3).
• The derivative of -4x^9 is -4*9*x^8 or -36x^8.
• The derivative of -11x is simply -11.
Combining these results, the final solution for f'(x) is: f'(x) = (2/3)*x^(-1/3) - 36x^8 - 11. Therefore, the derivative of the function f(x) = x^(2/3) - 4x^9 - 11x, denoted as f'(x), is found by applying the power rule and is f'(x) = (2/3)*x^(-1/3) - 36x^8 - 11.
