consider the functions f(x) and g(x), for which f(0)=6, g(0)=7, f'(0)=11, and g'(0)=-4. find h'(0) for the function h(x)=f(x)/g(x)

Answer 1

By the quotient rule, h'(x) = (f'g - g'f) / g², thus h'(0) = [11•7 - (-4)•6] / 7² = 101/49.