PART 13：例題-乘法法則

設 \(f(x) = \left( {\sqrt x  - 3} \right)\left( {{x^2} + x + 1} \right)\) ，試求 \(f'(1)\)

SOL:

\(f'(x) = \)\({\left( {\sqrt x  - 3} \right)^\prime }\left( {{x^2} + x + 1} \right)\)+\(\left( {\sqrt x  - 3} \right){\left( {{x^2} + x + 1} \right)^\prime }\)

　　　\( = \frac{1}{{2\sqrt x }}\left( {{x^2} + x + 1} \right)\)+\(\left( {\sqrt x  - 3} \right)\left( {2x + 1} \right)\)

\(f'(1) = \)\(\frac{1}{2}\left( 3 \right)\)+\(\left( { - 2} \right)\left( 3 \right)\)\( =- \frac{9}{2}\)