PART 15：例題-連鎖律

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

SOL:

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

\(f'(1) = 3{\left( 3 \right)^2}\left( 3 \right) = 81\)