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

解

導関数

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

9 (10 x^{4} + 100 x^{3} + 300 x^{2} + 250 x)

解答ステップ

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

定数を除去:

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

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

積の法則を適用:

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

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

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

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

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

= 9 (2 (x^{2} + 5 x) (2 x + 5) (2 x + 5) + 2 (x^{2} + 5 x)^{2})

簡素化

9 (2 (x^{2} + 5 x) (2 x + 5) (2 x + 5) + 2 (x^{2} + 5 x)^{2}) : 9 (10 x^{4} + 100 x^{3} + 300 x^{2} + 250 x)

= 9 (10 x^{4} + 100 x^{3} + 300 x^{2} + 250 x)