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Calculus grade 12

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differentiate the function (

a) y = cos³x

b) y = Sin²xCos3x

c) y = Sin (x³)

  • Calculus grade 12 -

    chain rule
    dy/dx = 3(cos^2 x)(-sinx)
    = -3sinx cos^2 x

    b) product rule
    dy/dx = (sin^2 x)(-3sin (3x) ) + (cos (3x))(2sinx(cosx))
    = ....

    c) you try it, let me know what you got

  • Calculus grade 12 -

    Hey Reiny, I think b) is wrong.
    I got:

    b)y' = 2SinxCos3x + CosxCos3x * (-Sinx)
    y' = 2SinxCos3x - SinxCosxCos3x

    ... and I am not sure how to do c)

  • Calculus grade 12 -

    don't know how you got your answer, I will stick to mine

    derivative of sin^2 x or (sinx)^2 is
    2sinx cosx
    the derivative of cos 3x = (-sin 3x)(3) = -3sin 3x

    so dy/dx = (sin^2 x)(-3sin (3x)) + cos(3x) (2sinxcosx)
    like I had
    all you have to do is trying to simplify it a bit.

    3rd one:
    y = sin (x^3)
    dy/dx = cos (x^3) (3x^2)
    = 3x^2 cos(x^3)

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