derivative of 3^{5x+2}

解

\frac{d}{d x} (3^{5 x + 2})

5 ln (3) \cdot 3^{5 x + 2}

解答ステップ

\frac{d}{d x} (3^{5 x + 2})

指数の規則を適用する:

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

3^{5 x + 2} = e^{(5 x + 2) l n (3)}

= \frac{d}{d x} (e^{(5 x + 2) l n (3)})

連鎖法則を適用:

e^{(5 x + 2) l n (3)} \frac{d}{d x} ((5 x + 2) ln (3))

= e^{(5 x + 2) l n (3)} \frac{d}{d x} ((5 x + 2) ln (3))

\frac{d}{d x} ((5 x + 2) ln (3)) = 5 ln (3)

= e^{(5 x + 2) l n (3)} \cdot 5 ln (3)

e^{(5 x + 2) l n (3)} = 3^{5 x + 2}

= 5 ln (3) \cdot 3^{5 x + 2}