derivative f(x)=x^{6x}

解

導関数

f (x) = x^{6 x}

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

解答ステップ

\frac{d}{d x} (x^{6 x})

指数の規則を適用する:

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

x^{6 x} = e^{6 x l n (x)}

= \frac{d}{d x} (e^{6 x l n (x)})

連鎖法則を適用:

e^{6 x l n (x)} \frac{d}{d x} (6 x ln (x))

= e^{6 x l n (x)} \frac{d}{d x} (6 x ln (x))

\frac{d}{d x} (6 x ln (x)) = 6 (ln (x) + 1)

= e^{6 x l n (x)} \cdot 6 (ln (x) + 1)

e^{6 x l n (x)} = x^{6 x}

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