derivative 2(3x^2ln(10x)+x^2)

解

導関数

2 (3 x^{2} ln (10 x) + x^{2})

2 (6 x ln (10 x) + 5 x)

解答ステップ

\frac{d}{d x} (2 (3 x^{2} ln (10 x) + x^{2}))

定数を除去:

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

= 2 \frac{d}{d x} (3 x^{2} ln (10 x) + x^{2})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 2 (\frac{d}{d x} (3 x^{2} ln (10 x)) + \frac{d}{d x} (x^{2}))

\frac{d}{d x} (3 x^{2} ln (10 x)) = 3 (2 x ln (10 x) + x)

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

= 2 (3 (2 x ln (10 x) + x) + 2 x)

拡張

3 (2 x ln (10 x) + x) + 2 x : 6 x ln (10 x) + 5 x

= 2 (6 x ln (10 x) + 5 x)