Question

Suppose

f(π/3) = 5 and f '(π/3) = −7,
and let
g(x) = f(x) sin x
and
h(x) = (cos x)/f(x).
FIND: g'(pi/3) AND h'(pi/3)

Answer 1

h'(1/8(7-2√3)

g'(1/2(2-7√3)

Answer 2

f(π/3) = 5
f '(π/3) = −7

g(x) = f(x) sin x
g'(x) = f(x) cos x + f'(x) sin x
g'(π/3) = f(π/3) cos (π/3) + f'(π/3) sin (π/3) = 5(1/2) - 7(√3/2) = (5 - 7√3)/2

h(x) = (cos x)/f(x).
h'(x) = (-f(x) sin x - f'(x) cos x) / (f(x))^2
h'(π/3) = (-f(π/3) sin (π/3) - f'(π/3) cos (π/3)) / (f(π/3))^2 = (-5(√3/2) + 7(1/2)) / 5^2 = (7 - 5√3) / 50