derivative of arcsinh(x^2)

解

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

\frac{2 x}{x ^{4} + 1}

解答ステップ

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

連鎖法則を適用:

\frac{1}{( x ^{2} ) ^{2} + 1} \frac{d}{d x} (x^{2})

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

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

= \frac{1}{( x ^{2} ) ^{2} + 1} \cdot 2 x

簡素化

\frac{1}{( x ^{2} ) ^{2} + 1} \cdot 2 x : \frac{2 x}{x ^{4} + 1}

= \frac{2 x}{x ^{4} + 1}