derivative e^{2x}(2x+3)^7

解

導関数

e^{2 x} (2 x + 3)^{7}

e^{2 x} \cdot 2 (2 x + 3)^{7} + 14 (2 x + 3)^{6} e^{2 x}

解答ステップ

\frac{d}{d x} (e^{2 x} (2 x + 3)^{7})

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{2 x}, g = (2 x + 3)^{7}

= \frac{d}{d x} (e^{2 x}) (2 x + 3)^{7} + \frac{d}{d x} ((2 x + 3)^{7}) e^{2 x}

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

\frac{d}{d x} ((2 x + 3)^{7}) = 14 (2 x + 3)^{6}

= e^{2 x} \cdot 2 (2 x + 3)^{7} + 14 (2 x + 3)^{6} e^{2 x}