Final answer:
To find f '(x) for the function f(x) = x² - 5x² + 9x³, we need to find the derivative of each term separately and then add them up.
Step-by-step explanation:
To find f '(x) for the function f(x) = x² - 5x² + 9x³, we need to find the derivative of each term separately and then add them up.
The derivative of x² is 2x, the derivative of -5x² is -10x, and the derivative of 9x³ is 27x².
Adding these derivatives together gives us the derivative of the entire function:
f '(x) = 2x - 10x + 27x²