Question

Suppose that f(x) and g(x) are differentiable functions such that f(2) = 3, f'(2) = 7, g(2) = 8, and g'(2) = 6. Find h'(2) when h(x) = f(x) / g(x).

Answer 1

To find h'(2) when h(x) = f(x) / g(x), we can use the quotient rule and substitute the given values.

Step-by-step explanation:

To find the derivative of h(x) = f(x) / g(x), we can use the quotient rule. The quotient rule states that if we have a function of the form h(x) = u(x) / v(x), then the derivative is given by:

h'(x) = (u'(x)v(x) - u(x)v'(x)) / (v(x))^2

So for the given problem, we have:

h'(x) = (f'(x)g(x) - f(x)g'(x)) / (g(x))^2

Substituting the given values, we get:

h'(2) = (7 * 8 - 3 * 6) / (8)^2 = -2/16 = -1/8