derivative x^{11}arcsin(x)

解

導関数

x^{11} arcsin (x)

11 x^{10} arcsin (x) + \frac{x ^{11}}{1 - x ^{2}}

解答ステップ

\frac{d}{d x} (x^{11} arcsin (x))

積の法則を適用:

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

f = x^{11}, g = arcsin (x)

= \frac{d}{d x} (x^{11}) arcsin (x) + \frac{d}{d x} (arcsin (x)) x^{11}

\frac{d}{d x} (x^{11}) = 11 x^{10}

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

= 11 x^{10} arcsin (x) + \frac{1}{1 - x ^{2}} x^{11}

\frac{1}{1 - x ^{2}} x^{11} = \frac{x ^{11}}{1 - x ^{2}}

= 11 x^{10} arcsin (x) + \frac{x ^{11}}{1 - x ^{2}}