calculus
posted by theo .
Find the derivative of the function. h(x) = (cos x/ 1+sin x)4

assume you mean
h = [cos (x)/(1+sin x)]^4
let z = [cos (x)/(1+sin x)]
then
dh/dz = 4 z^3
dh/dx = dh/dz * dz/dx
dh/dx = 4 [cos (x)/(1+sin x)]^3 d/dx[[cos (x)/(1+sin x)]
d/dx[cos (x)/(1+sin x)] = [(1+sin x)(sin x) cos^2x] / (1+sin x)^2
= [sin x 1]/(1+sin x)^2 = 1/(1+sin x)
so
dh/dx = 4 [cos (x)/(1+sin x)]^3 (1)/(1+sin x)
= 4 cos x/ (1+sin x)^4