derivative y=x^{4x}

解

導関数

y = x^{4 x}

4 x^{4 x} (ln (x) + 1)

解答ステップ

\frac{d}{d x} (x^{4 x})

指数の規則を適用する:

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

x^{4 x} = e^{4 x l n (x)}

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

連鎖法則を適用:

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

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

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

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

e^{4 x l n (x)} = x^{4 x}

= 4 x^{4 x} (ln (x) + 1)