derivative x^{x^3-2x}

解

導関数

x^{x^{3} - 2 x}

x^{x^{3} - 2 x} (ln (x) (3 x^{2} - 2) + x^{2} - 2)

解答ステップ

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

指数の規則を適用する:

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

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

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

連鎖法則を適用:

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

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

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

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

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

= x^{x^{3} - 2 x} (ln (x) (3 x^{2} - 2) + x^{2} - 2)