derivative 4^{x+1}

解

導関数

4^{x + 1}

ln (2) \cdot 2^{2 x + 3}

解答ステップ

\frac{d}{d x} (4^{x + 1})

指数の規則を適用する:

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

4^{x + 1} = e^{(x + 1) l n (4)}

= \frac{d}{d x} (e^{(x + 1) l n (4)})

連鎖法則を適用:

e^{(x + 1) l n (4)} \frac{d}{d x} ((x + 1) ln (4))

= e^{(x + 1) l n (4)} \frac{d}{d x} ((x + 1) ln (4))

\frac{d}{d x} ((x + 1) ln (4)) = 2 ln (2)

= e^{(x + 1) l n (4)} \cdot 2 ln (2)

簡素化

e^{(x + 1) l n (4)} \cdot 2 ln (2) : ln (2) \cdot 2^{2 x + 3}

= ln (2) \cdot 2^{2 x + 3}