PART 14：例題-除法法則

設 \(f(x) = \frac{{{x^2} + x + 1}}{{x - 2}}\) ，試求 \(f'(0)\)

SOL:

\(f'(x) = \frac{{{{\left( {{x^2} + x + 1} \right)}^\prime }\left( {x - 2} \right) - \left( {{x^2} + x + 1} \right){{\left( {x - 2} \right)}^\prime }}}{{{{\left( {x - 2} \right)}^2}}}\)\( = \frac{{\left( {2x + 1} \right)\left( {x - 2} \right) - \left( {{x^2} + x + 1} \right)}}{{{{\left( {x - 2} \right)}^2}}}\)

\(f'(0) = \frac{{\left( 1 \right)\left( { - 2} \right) - \left( 1 \right)}}{4} = - \frac{3}{4}\)