(\partial)/(\partial x)(x^{2x})

解

\frac{\partial}{\partial x} (x^{2 x})

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

解答ステップ

\frac{\partial}{\partial 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)}

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

連鎖法則を適用:

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

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

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

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

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

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