Question

The table above gives the values of the differentiable functions f and g and their derivatives at x = a. What is the value of d(f/g)/dx at x = a?

Answer 1

The value of d(f/g)/dx at x = a is f’(a)g’(a)-f(a)g’’(a).

Step-by-step explanation:

To find the derivative of the fraction f/g with respect to x, we can use the chain rule. The derivative of f with respect to x is f’(x), and the derivative of g with respect to x is g’(x). Therefore, the derivative of f/g with respect to x is:

d(f/g)/dx = f’(x)g’(x) - f(x)g’’(x)

Since we are given the values of f and g and their derivatives at x = a, we can plug these values into the above equation to get:

d(f/g)/dx at x = a = f’(a)g’(a) - f(a)g’’(a)

Therefore, the value of d(f/g)/dx at x = a is f’(a)g’(a) - f(a)g’’(a).