Final answer:
To find the derivative of the function f(x) = ax^2 + (4/x) - 3, use the power rule and the quotient rule.
Step-by-step explanation:
To find the derivative of the function f(x) = ax^2 + (4/x) - 3, we will use the power rule and the quotient rule.
The power rule states that the derivative of x^n is nx^(n-1). So, the derivative of ax^2 is 2ax.
The quotient rule states that the derivative of (u/v) is (vu' - uv') / v^2. In this case, u = 4 and v = x. Therefore, the derivative of (4/x) is ((x)(0) - (4)(1)) / x^2 = -4/x^2.
Since the derivative of -3 is 0, the derivative of the entire function f(x) = ax^2 + (4/x) - 3 is f'(x) = 2ax - 4/x^2.