Tìm đạo hàm của hàm số \(y = \left( {x + 1} \right){\left( {x + 2} \right)^2}{\left( {x + 3} \right)^3}\)
\(\begin{array}{l}
y = (x + 1){(x + 2)^2}{(x + 3)^3}\\
\Rightarrow y\prime = {(x + 2)^2}{(x + 3)^3} + (x + 1)[2(x + 2){(x + 3)^3} + {(x + 2)^2}.3{(x + 3)^2}]\\
= {(x + 2)^2}{(x + 3)^3} + (x + 1)(x + 2){(x + 3)^2}[2(x + 3) + 3(x + 2)]\\
= {(x + 2)^2}{(x + 3)^3} + (x + 1)(x + 2){(x + 3)^2}(5x + 12)\\
= (x + 2){(x + 3)^2}({x^2} + 5x + 6 + 5{x^2} + 17x + 12)\\
= (x + 2){(x + 3)^2}(6{x^2} + 22x + 18)
\end{array}\)
-- Mod Toán 11