Question

suppose f(pi/3)=4 and f'(pi/3)=(-3). 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' (x) = f(x) cos x + f'(x) sin x = 4 cos (pi/3) - 3 sin (pi/3)
= 4 (1/2) - 3* sqrt3 / 2

h' = [ -f(x)sin x - f'(x) cos x ] / [ f(x) ]^2
same way now