derivative of 2x^{3x}

解

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

6 x^{3 x} (ln (x) + 1)

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (x^{3 x})

指数の規則を適用する:

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

x^{3 x} = e^{3 x l n (x)}

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

連鎖法則を適用:

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

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

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

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

簡素化

2 e^{3 x l n (x)} \cdot 3 (ln (x) + 1) : 6 x^{3 x} (ln (x) + 1)

= 6 x^{3 x} (ln (x) + 1)