derivative of (7^{10x+1})

解

\frac{d}{d x} ((7)^{10 x + 1})

10 ln (7) \cdot 7^{10 x + 1}

解答ステップ

\frac{d}{d x} ((7)^{10 x + 1})

指数の規則を適用する:

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

7^{10 x + 1} = e^{(10 x + 1) l n (7)}

= \frac{d}{d x} (e^{(10 x + 1) l n (7)})

連鎖法則を適用:

e^{(10 x + 1) l n (7)} \frac{d}{d x} ((10 x + 1) ln (7))

= e^{(10 x + 1) l n (7)} \frac{d}{d x} ((10 x + 1) ln (7))

\frac{d}{d x} ((10 x + 1) ln (7)) = 10 ln (7)

= e^{(10 x + 1) l n (7)} \cdot 10 ln (7)

e^{(10 x + 1) l n (7)} = 7^{10 x + 1}

= 10 ln (7) \cdot 7^{10 x + 1}