derivative 126x(9x^2+6)^6

解

導関数

126 x (9 x^{2} + 6)^{6}

126 ((9 x^{2} + 6)^{6} + 108 x^{2} (9 x^{2} + 6)^{5})

解答ステップ

\frac{d}{d x} (126 x (9 x^{2} + 6)^{6})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 126 \frac{d}{d x} (x (9 x^{2} + 6)^{6})

積の法則を適用:

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

f = x, g = (9 x^{2} + 6)^{6}

= 126 (\frac{d x}{d x} (9 x^{2} + 6)^{6} + \frac{d}{d x} ((9 x^{2} + 6)^{6}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} ((9 x^{2} + 6)^{6}) = 108 x (9 x^{2} + 6)^{5}

= 126 (1 \cdot (9 x^{2} + 6)^{6} + 108 x (9 x^{2} + 6)^{5} x)

簡素化

126 (1 \cdot (9 x^{2} + 6)^{6} + 108 x (9 x^{2} + 6)^{5} x) : 126 ((9 x^{2} + 6)^{6} + 108 x^{2} (9 x^{2} + 6)^{5})

= 126 ((9 x^{2} + 6)^{6} + 108 x^{2} (9 x^{2} + 6)^{5})