Suppose that f(5)=1, f'(5)=8, g(5)=-6, and g'(5)=2. Find the following values. (a) (fg)'(5) (b) (f/g)'(5) (c) (g/f)'(5)

Answer 1

(a)

(fg)'(5) = (f'g + fg')(5) = f'(5)g(5) + f(5)g'(5) = 8×(-6) + 1×2 = -46

(b)

(f/g)'(5) = ((f'g - fg')/g²)(5) = ((f'(5)g(5) - f(5)g'(5))/g²(5)) = (8×(-6) - 1×2)/(-6)² = -25/16

(c)

(g/f)'(5) = ((g'f - gf')/f²)(5) = ((g'(5)f(5) - g(5)f'(5))/f²(5)) = (2×1 - (-6)×8)/1² = 50