derivative of (1-3xarccoth(3x))

解

\frac{d}{d x} ((1 - 3 x) arccoth (3 x))

- 3 arccoth (3 x) + \frac{3}{3 x + 1}

解答ステップ

\frac{d}{d x} ((1 - 3 x) arccoth (3 x))

積の法則を適用:

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

f = 1 - 3 x, g = arccoth (3 x)

= \frac{d}{d x} (1 - 3 x) arccoth (3 x) + \frac{d}{d x} (arccoth (3 x)) (1 - 3 x)

\frac{d}{d x} (1 - 3 x) = - 3

\frac{d}{d x} (arccoth (3 x)) = \frac{3}{1 - 9 x ^{2}}

= (- 3) arccoth (3 x) + \frac{3}{1 - 9 x ^{2}} (1 - 3 x)

簡素化

(- 3) arccoth (3 x) + \frac{3}{1 - 9 x ^{2}} (1 - 3 x) : - 3 arccoth (3 x) + \frac{3}{3 x + 1}

= - 3 arccoth (3 x) + \frac{3}{3 x + 1}