derivative y=(x^2+3)((2x+5)^6)

解

導関数

y = (x^{2} + 3) ((2 x + 5)^{6})

2 x (2 x + 5)^{6} + 12 (2 x + 5)^{5} (x^{2} + 3)

解答ステップ

\frac{d}{d x} ((x^{2} + 3) (2 x + 5)^{6})

積の法則を適用:

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

f = x^{2} + 3, g = (2 x + 5)^{6}

= \frac{d}{d x} (x^{2} + 3) (2 x + 5)^{6} + \frac{d}{d x} ((2 x + 5)^{6}) (x^{2} + 3)

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

\frac{d}{d x} ((2 x + 5)^{6}) = 12 (2 x + 5)^{5}

= 2 x (2 x + 5)^{6} + 12 (2 x + 5)^{5} (x^{2} + 3)