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Calculus

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Differentiate each function

a) y = Cos³ x

b) y = Sin(x³)

c) y = Sin²xCos3x

  • Calculus -

    a)
    let z = cos x then dz/dx = -sin x
    y = z^3
    y' = 3 z^2 dz/dx
    y' = 3 cos^2 x (-sin x)
    = -3 sin x cos^2 x

  • Calculus -

    b)
    let z = x^3 then dz/dx = 3 x^2
    y = sin z
    y' = cos z dz/dx
    = cos(x^3) (3 x^2)
    = 3 x^2 cos x^3

  • Calculus -

    c)y' = sin^2 x (-3sin 3x)+ cos 3x (2 sin x cos x

    = -3sin 3x sin^2 x + 2 cos 3x sin x cos x

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