derivative derivative of 2^{ln(x})

解

導関数

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

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

解答ステップ

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

指数の規則を適用する:

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

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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