If f and g are differentiable functions for all real values of x such that f(1) = 4, g(1) = 3, f '(3) = −5, f '(1) = −4, g '(1) = −3, g '(3) = 2, then find h '(1) if h(x) = the quotient of f of x and g of x.

h'(1)=0

Step-by-step explanation:

We use the definition of the derivative of a quotient:

If , then:

Since in our case we want the derivative of at the point x = 1, which is indicated by: h'(1), we need to evaluate the previous expression at x = 1, that is:

which, by replacing with the given numerical values:

becomes: