Let f(7)=0, f'(7)=14, g(7)=1, g'(7)=1/7. Find h'(7) if h(x)=f(x)/g(x)

Answer 1

Just use the quotient rule:

h' = (f'g - fg')/g^2
= (14*1 - 0*1/7)/1^2 = 14