derivative 12^{9x}

解

導関数

1 2^{9 x}

ln (12) \cdot 26214 4^{x} \cdot 3^{9 x + 2}

解答ステップ

\frac{d}{d x} (1 2^{9 x})

指数の規則を適用する:

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

1 2^{9 x} = e^{9 x l n (12)}

= \frac{d}{d x} (e^{9 x l n (12)})

連鎖法則を適用:

e^{9 x l n (12)} \frac{d}{d x} (9 x ln (12))

= e^{9 x l n (12)} \frac{d}{d x} (9 x ln (12))

\frac{d}{d x} (9 x ln (12)) = 9 ln (12)

= e^{9 x l n (12)} \cdot 9 ln (12)

簡素化

e^{9 x l n (12)} \cdot 9 ln (12) : ln (12) \cdot 26214 4^{x} \cdot 3^{9 x + 2}

= ln (12) \cdot 26214 4^{x} \cdot 3^{9 x + 2}