is rule states that the derivative of a composite function is the product of the derivatives of the separate functions. nportantly, the derivative of the inner function is evaluatet at the value of x. and derivative of the outer function is evaluatet at the functional value of the inner function evaluated at x. For example, if f(x) and g(y) are given as f (x) = 8(x - 7)2 - 2 and g(y) = 7y + 4y To find the derivative of g(f (x)) at x = 8, we evaluate the derivative f' at x = 8 and the derivative g at y = 7 X The value for the derivative f is 7 x . Overall, the derivative of g(f (x)) evaluated at x = 8 is equal to 7 X