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Calculus grade 12

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Determine the derivative of the function (² = square):

a) y = (x² + x - 1)Sin²x

b) y = (x² + 1)/Sin²x

  • Calculus grade 12 -

    chain rule:
    d/dx sin^2 x = 2(sinx)(cosx) = sin2x

    a)
    y = (x^2+x-1)sin^2 x
    y' = (2x+1)sin^2 x + (x^2+x-1)sin2x

    b)
    y = (x^2+1)/sin^2 x
    y = (2x*sin^2 x - (x^2+1)*2*sinx*cosx]/sin^4 x
    = [2x*sinx - (x^2+1)*cosx]/sin^3 x

  • Calculus grade 12 -

    Thank you Steve

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