Answer
(a) F′(2) = 10
(b) F′(2) = 19
(c) F′(2) = 9
(d) F′(2) =-1
Work Step by Step
(a) F(x) = 5f(x) + 2g(x), F′(2) = 5(4) + 2(−5) = 10.
(b) F(x) = f(x) − 3g(x), F′(2) = 4 − 3(−5) = 19.
(c) F(x) = f(x)g(x) + g(x)f(x), F′(2) = (−1)(−5) + (1)(4) = 9.
(d) F(x) = [g(x)f(x) − f(x)g(x)]/g2(x), F′(2) = [(1)(4) − (−1)(−5)]/(1)2 = −1.
