derivative of 5x^{2x}

解

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

10 x^{2 x} (ln (x) + 1)

解答ステップ

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

定数を除去:

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

= 5 \frac{d}{d x} (x^{2 x})

指数の規則を適用する:

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

x^{2 x} = e^{2 x l n (x)}

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

連鎖法則を適用:

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

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

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

= 5 e^{2 x l n (x)} \cdot 2 (ln (x) + 1)

簡素化

5 e^{2 x l n (x)} \cdot 2 (ln (x) + 1) : 10 x^{2 x} (ln (x) + 1)

= 10 x^{2 x} (ln (x) + 1)