derivative of 3^{4x+1}

解

\frac{d}{d x} (3^{4 x + 1})

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

解答ステップ

\frac{d}{d x} (3^{4 x + 1})

指数の規則を適用する:

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

3^{4 x + 1} = e^{(4 x + 1) l n (3)}

= \frac{d}{d x} (e^{(4 x + 1) l n (3)})

連鎖法則を適用:

e^{(4 x + 1) l n (3)} \frac{d}{d x} ((4 x + 1) ln (3))

= e^{(4 x + 1) l n (3)} \frac{d}{d x} ((4 x + 1) ln (3))

\frac{d}{d x} ((4 x + 1) ln (3)) = 4 ln (3)

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