AP03-04

retour

$\begin{aligned} f_{1}^{'} (x) & = 2 x e^{x} + x^{2} e^{x} = (2 x + x^{2}) e^{x}; \\ f_{2}^{'} (x) & = \frac{1 \times (x^{2} + 1) - (x - 3) \times (2 x)}{(x^{2} + 1)^{2}} \\ = \frac{x^{2} + 1 - 2 x^{2} + 6 x}{(x^{2} + 1)^{2}} = \frac{- x^{2} + 6 x + 1}{(x^{2} + 1)^{2}}; \\ f_{3}^{'} (x) & = (2 \times 2 x + 5) e^{2 x^{2} + 5 x} = (4 x + 5) e^{2 x^{2} + 5 x}; \\ f_{4}^{'} (x) & = 6 \times 2 (2 x - 11)^{5} = 12 (2 x - 11)^{5} . \end{aligned}$

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code : 173