Question

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

Answer 1

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