derivative 48x(4x^2+9)^5

解

導関数

48 x (4 x^{2} + 9)^{5}

48 ((4 x^{2} + 9)^{5} + 40 x^{2} (4 x^{2} + 9)^{4})

解答ステップ

\frac{d}{d x} (48 x (4 x^{2} + 9)^{5})

定数を除去:

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

= 48 \frac{d}{d x} (x (4 x^{2} + 9)^{5})

積の法則を適用:

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

f = x, g = (4 x^{2} + 9)^{5}

= 48 (\frac{d x}{d x} (4 x^{2} + 9)^{5} + \frac{d}{d x} ((4 x^{2} + 9)^{5}) x)

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

\frac{d}{d x} ((4 x^{2} + 9)^{5}) = 40 x (4 x^{2} + 9)^{4}

= 48 (1 \cdot (4 x^{2} + 9)^{5} + 40 x (4 x^{2} + 9)^{4} x)

簡素化

48 (1 \cdot (4 x^{2} + 9)^{5} + 40 x (4 x^{2} + 9)^{4} x) : 48 ((4 x^{2} + 9)^{5} + 40 x^{2} (4 x^{2} + 9)^{4})

= 48 ((4 x^{2} + 9)^{5} + 40 x^{2} (4 x^{2} + 9)^{4})