derivative of 10^{2x-1}

解

\frac{d}{d x} (1 0^{2 x - 1})

ln (10) \cdot 4^{x} \cdot 5^{2 x - 1}

解答ステップ

\frac{d}{d x} (1 0^{2 x - 1})

指数の規則を適用する:

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

1 0^{2 x - 1} = e^{(2 x - 1) l n (10)}

= \frac{d}{d x} (e^{(2 x - 1) l n (10)})

連鎖法則を適用:

e^{(2 x - 1) l n (10)} \frac{d}{d x} ((2 x - 1) ln (10))

= e^{(2 x - 1) l n (10)} \frac{d}{d x} ((2 x - 1) ln (10))

\frac{d}{d x} ((2 x - 1) ln (10)) = 2 ln (10)

= e^{(2 x - 1) l n (10)} \cdot 2 ln (10)

簡素化

e^{(2 x - 1) l n (10)} \cdot 2 ln (10) : ln (10) \cdot 4^{x} \cdot 5^{2 x - 1}

= ln (10) \cdot 4^{x} \cdot 5^{2 x - 1}