derivative of 10^{nx}

解

\frac{d}{d x} (1 0^{n x})

ln (10) \cdot 1 0^{n x} n

解答ステップ

\frac{d}{d x} (1 0^{n x})

指数の規則を適用する:

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

1 0^{n x} = e^{n x l n (10)}

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

連鎖法則を適用:

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

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

\frac{d}{d x} (n x ln (10)) = ln (10) n

= e^{n x l n (10)} ln (10) n

e^{n x l n (10)} = 1 0^{n x}

= ln (10) \cdot 1 0^{n x} n