Suppose f(pi/3) = 3 and f '(pi/3) = −7,

Question

and let g(x) = f(x) sin x and
h(x) = (cos x)/f(x). Find the following.

a. g'(pi/3)

b. h'(pi/3)

Answer 1

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

h = cos(x)/f
h' = (-sin(x)*f - cos(x)*f')/f^2
h'(pi/3) = [(-√3/2)*3 - (1/2)(-7)]/9 = (7-3√3)/18

Answer 2

Thank you very much sir and Good Day!