derivative y=x^3(2x+3)^7

解

導関数

y = x^{3} (2 x + 3)^{7}

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

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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