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Schminder
Schminder asked in Science & MathematicsMathematics · 7 years ago

derivative of cos(x)sin(x) proof?

Can someone show how the derivative of cos(x)sin(x) = cos(2x)?

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  • Rogue
    Lv 7
    7 years ago
    Favorite Answer

    d/dx(cos(x)sin(x))

    using the product rule d/dx(uv) = u * dv/dx + v * du/dx

    => cos(x) * d/dx(sin(x)) + sin(x) * d/dx(cos(x))

    given d/dx(sin(x)) = cos(x)

    => cos^2(x) + sin(x) * d/dx(cos(x))

    given d/dx(cos(x)) = -sin(x)

    => cos^2(x) − sin^2(x)

    given cos(2θ) = cos^2(θ) − sin^2(θ)

    => cos(2x)

  • ?
    Lv 7
    7 years ago

    Note that ( sin 2x ) /2 = cos(x)sin(x)

    Differential of ( sin 2x ) /2 = cos(2x)

  • Como
    Lv 7
    7 years ago

    f (x) = cos x sin x

    f ` (x) = (-sin x) ( sin x) + (cos x) ( cos x)

    f ` (x) = cos²x - sin²x = cos 2x

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