Question

Can someone please show me how to do this!!! The table above gives values for the functions f and g and their derivatives at x = 3. Let k be the function given by k (x) = f(x)/g(x), where g (x) is not equal to 0. What is the value of k’?

Answer 1

To find the value of k', use the quotient rule formula with the given values of f(x), g(x), f'(x), and g'(x).

Step-by-step explanation:

To find the value of k', we need to differentiate the expression k(x) = f(x) / g(x). Let's call f'(x) the derivative of f(x) and g'(x) the derivative of g(x). The quotient rule states that (f(x) / g(x))' = (f'(x) * g(x) - f(x) * g'(x)) / (g(x))^2. Using the values of f(x), g(x), f'(x), and g'(x) given in the table, we can substitute them into the quotient rule formula to find k'(x).