derivative f(x)=6xln(3x^2-10)

解

導関数

f (x) = 6 x ln (3 x^{2} - 10)

6 (ln (3 x^{2} - 10) + \frac{6 x ^{2}}{3 x ^{2} - 10})

解答ステップ

\frac{d}{d x} (6 x ln (3 x^{2} - 10))

定数を除去:

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

= 6 \frac{d}{d x} (x ln (3 x^{2} - 10))

積の法則を適用:

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

f = x, g = ln (3 x^{2} - 10)

= 6 (\frac{d x}{d x} ln (3 x^{2} - 10) + \frac{d}{d x} (ln (3 x^{2} - 10)) x)

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

\frac{d}{d x} (ln (3 x^{2} - 10)) = \frac{6 x}{3 x ^{2} - 10}

= 6 (1 \cdot ln (3 x^{2} - 10) + \frac{6 x}{3 x ^{2} - 10} x)

簡素化

6 (1 \cdot ln (3 x^{2} - 10) + \frac{6 x}{3 x ^{2} - 10} x) : 6 (ln (3 x^{2} - 10) + \frac{6 x ^{2}}{3 x ^{2} - 10})

= 6 (ln (3 x^{2} - 10) + \frac{6 x ^{2}}{3 x ^{2} - 10})