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Câu hỏi: Tìm đạo hàm của hàm số sau:
\(y = \left( {x + 1} \right){\left({x + 2} \right)^2}{\left({x + 3} \right)^3}.\)
\(y = \left( {x + 1} \right){\left({x + 2} \right)^2}{\left({x + 3} \right)^3}.\)
Lời giải chi tiết
\(\begin{array}{l}
y' = \left({x + 1} \right)'{\left({x + 2} \right)^2}{\left({x + 3} \right)^3}\\
+ \left({x + 1} \right)\left[ {{{\left({x + 2} \right)}^2}} \right]'{\left({x + 3} \right)^3}\\
+ \left({x + 1} \right){\left({x + 2} \right)^2}\left[ {{{\left({x + 3} \right)}^3}} \right]'\\
= {\left({x + 2} \right)^2}{\left({x + 3} \right)^3}\\
+ \left({x + 1} \right). 2\left({x + 2} \right){\left({x + 3} \right)^3}\\
+ \left({x + 1} \right){\left({x + 2} \right)^2}. 3{\left({x + 3} \right)^2}
\end{array}\)
\(\begin{array}{l}
y' = \left({x + 1} \right)'{\left({x + 2} \right)^2}{\left({x + 3} \right)^3}\\
+ \left({x + 1} \right)\left[ {{{\left({x + 2} \right)}^2}} \right]'{\left({x + 3} \right)^3}\\
+ \left({x + 1} \right){\left({x + 2} \right)^2}\left[ {{{\left({x + 3} \right)}^3}} \right]'\\
= {\left({x + 2} \right)^2}{\left({x + 3} \right)^3}\\
+ \left({x + 1} \right). 2\left({x + 2} \right){\left({x + 3} \right)^3}\\
+ \left({x + 1} \right){\left({x + 2} \right)^2}. 3{\left({x + 3} \right)^2}
\end{array}\)