Final answer:
To find the derivative of the function f(x) = 7 + 4/x + 1/6x², we can use the power rule for differentiation. The derivative is -4/x^2 + x/3
Step-by-step explanation:
To find the derivative of the function f(x) = 7 + 4/x + 1/6x², we can use the power rule for differentiation. The power rule states that the derivative of x^n is equal to n*x^(n-1). Applying this rule to each term in the function, we get:
f'(x) = 0 + (-4/x^2) + (1/6)*(2x) = -4/x^2 + 2x/6 = -4/x^2 + x/3