Suppose that f(2) = 5, f '(2) = 5, g(2) = -6, and g'(2) = 4.
Find the following values: (fg)'(2); (f/g)'(2); (g/f)'(2)
(fg)' = f'.g + f.g'
at x = 2, (fg)' = f'(2).g(2) + f(2).g'(2)
(fg)' = 5.(-6) + 5.4 = -30 + 20
(fg)' = -10
(f/g)' = (g.f' - f.g')/g^2
(f/g)'(2) = (g(2).f'(2) - f(2).(g'(2))/g(2)^2
(f/g)'(2) = (-6.5 - 5.4)/(-6)^2
(f/g)' = (-30 - 20)/36 = -50/36
(f/g)' = -25/18
(g/f)' = (f.g' - g.f')/f^2
(g/f)'(2) = (f(2).g'(2) - g(2).(f'(2))/f(2)^2
(g/f)'(2) = (5.4 – (-6).5)/(5)^2
(g/f)' = (20 + 30)/25 = 50/25
(g/f)' = 2