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Find the derivative of f. you may simplify before differentiating

f(x)= x2-7x+12/x4-8x3+13x2+30x-72

  • Calculus -

    Surely you meant ...

    f(x) = (x^2-7x+12)/(x^4-8x^3+13x^2+30x-72)
    = (x-3)(x-4)/(x^4-8x^3+13x^2+30x-72)
    I checked by synthetic division if those factors are contained in the denominator, and they are, so
    = 1/(x^2 - x - 6)
    = (x^2 - x - 6)^-1

    f '(x) = -(x^2 - x - 6)^-2 (2x-1)

    = (1 - 2x)/(x^2 - x - 6)^2

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