derivative 17^{x-1}

解

導関数

1 7^{x - 1}

ln (17) \cdot 1 7^{x - 1}

解答ステップ

\frac{d}{d x} (1 7^{x - 1})

指数の規則を適用する:

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

1 7^{x - 1} = e^{(x - 1) l n (17)}

= \frac{d}{d x} (e^{(x - 1) l n (17)})

連鎖法則を適用:

e^{(x - 1) l n (17)} \frac{d}{d x} ((x - 1) ln (17))

= e^{(x - 1) l n (17)} \frac{d}{d x} ((x - 1) ln (17))

\frac{d}{d x} ((x - 1) ln (17)) = ln (17)

= e^{(x - 1) l n (17)} ln (17)

e^{(x - 1) l n (17)} = 1 7^{x - 1}

= ln (17) \cdot 1 7^{x - 1}