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find the derivative of f(x)=cot(3x)csc^2(3x)

  • calculus -

    f(x)=cot(3x)csc^2(3x) = cosx/sin^3x

    Let sinx = u . Then du = cosx dx

    The integral of f(x) becomes

    Integral of du/u^3 = -(1/2) u^-2
    = (-1/2)(1/sinx)^2
    = (-1/2)csc^2x

  • calculus -

    first change it to
    f(x) = cos 3x/(sin 3x)^3 like drwls had

    now use the quotient rule to find f'(x)

    f'(x) = [(sin 3x)^3(-3)(sin 3x) - 3(sin 3x)^2(cos 3x)(3)(cos 3x)]/(sin 3x)^6
    = -3[(sin 3x)^2 + 3(cos 3x)^2]/(sin 3x)^4

  • calculus -

    I made at least one mistake. The first was using x instead of 3x.

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