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Find f'(x) if f(x)= Logx(x^2-5x+6)

that logx is a sub x

  • Calculus -

    let y = logx (x^2 - 5x + 6)
    x^y = x^2 - 5x + 6
    ln both sides

    ln (x^y) = ln(x^2 - 5x + 6)
    y lnx = ln(x^2 - 5x + 6)
    differentiate implicityly
    y(1/x) + (lnx) dy/dx = (2x-5)/(x^2-5x+6)

    dy/dx = ((2x-5)/(x^2-5x+6) - y/x)/lnx

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