Suppose that f(5) = 2, f'(5) = 3, g(5) = -6, and g'(5) = 1. Find the following values:
(f/g)'(5)

1 Answers

Best Answer

(1)Rewrite the function as a quotient.
(f/g)(x)=(f(x))/(g(x))
(2)Find the derivative using the quotient rule.
(f/g)'(x)=(f'(x)g(x)-f(x)g'(x))/([g(x)]^(2))
(3)Substitute x=5.
(f/g)'(5)=(f'(5)g(5)-f(5)g'(5))/([g(5)]^(2))
Substitute f'(5)=3, g(5)=-6, f(5)=2, and g'(5)=1.
=(3(-6)-2(1))/((-6)^(2))
(5)Simplify
=(-20)/(36)
(6)Reduce the tion.
=-(5)/(9)