Find h'(0) for the function h(x)= (f(x)/g(x))?

Question

Consider the functions f(x) and g(x), for which
f(0)=3
g(0)=8
f '(0)=9
g'(0)=-6

Answer 1

h' (x) = [f'(x)*g(x) - f(x)*g'(x)] / (g(x))²
h'(0) = [9*8 - 3*(-6)] / (8)²
h'(0) = 90/64 = 45/32

Answer 2

In general it would be
h'(x) = (f'(x)g(x) - g'(x)f(x))/(f(x))²

HTH

Doug

Answer 3

(u/V)={[u'V-uV']/V²}