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calculus

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

  • calculus -

    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

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