derivative of 2^{arcsech(x})

解

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

- \frac{ln ( 2 ) \cdot 2 ^{arcsech (x)}}{x x + 1 - x + 1}

解答ステップ

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

指数の規則を適用する:

a^{b} = e^{b l n (a)}

2^{arcsech (x)} = e^{arcsech (x) l n (2)}

= \frac{d}{d x} (e^{arcsech (x) l n (2)})

連鎖法則を適用:

e^{arcsech (x) l n (2)} \frac{d}{d x} (arcsech (x) ln (2))

= e^{arcsech (x) l n (2)} \frac{d}{d x} (arcsech (x) ln (2))

\frac{d}{d x} (arcsech (x) ln (2)) = - \frac{ln ( 2 )}{x x + 1 - x + 1}

= e^{arcsech (x) l n (2)} (- \frac{ln ( 2 )}{x x + 1 - x + 1})

簡素化

e^{arcsech (x) l n (2)} (- \frac{ln ( 2 )}{x x + 1 - x + 1}) : - \frac{ln ( 2 ) \cdot 2 ^{arcsech (x)}}{x x + 1 - x + 1}

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