derivative 2^{x-1}

解

導関数

2^{x - 1}

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

解答ステップ

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

指数の規則を適用する:

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

2^{x - 1} = e^{(x - 1) l n (2)}

= \frac{d}{d x} (e^{(x - 1) l n (2)})

連鎖法則を適用:

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

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

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

= e^{(x - 1) l n (2)} ln (2)

e^{(x - 1) l n (2)} = 2^{x - 1}

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