derivative sqrt(1-9x^2)arccos(3x)

解

導関数

1 - 9 x^{2} arccos (3 x)

- \frac{9 x arccos ( 3 x )}{1 - 9 x ^{2}} - 3

解答ステップ

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

積の法則を適用:

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

f = 1 - 9 x^{2}, g = arccos (3 x)

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

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

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

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

簡素化

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

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