Given f(5)=3, f′(5)=7, g(5)=−1, and g′(5)=8, find the values of the following.

Question

Given f(5)=3, f′(5)=7, g(5)=−1, and g′(5)=8, find the values of the following.

(a) (fg) '(5) =

(b) (f/g) '(5) =

Answer 1

(fg)’(5)= f’(5)g(5) - f(5)g’(5) = -7 -24= -31.

(f/g)’(5)=( f’(5)g(5) - f(5)g’(5) )/ g(5)^2 = -31/(-1)^2 = -31.