Final answer:
The derivative of the function f(x) = x³ is found using the power rule of differentiation, resulting in f'(x) = 3x².
Step-by-step explanation:
To find the derivative of the function f(x) = x³, we apply the power rule of differentiation, which states that if f(x) = x^n, then f'(x) = nx^(n-1). Applying this rule to our function, we get:
f'(x) = 3 * x^(3-1) = 3x².
Therefore, the derivative of f(x) with respect to x is 3x², which corresponds to option a) 3x².