derivative of 4^{ln(x})

解

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

2 ln (2) x^{2 l n (2) - 1}

解答ステップ

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

指数の規則を適用する:

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

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

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

連鎖法則を適用:

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

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

\frac{d}{d x} (ln (x) ln (4)) = \frac{2 ln ( 2 )}{x}

= e^{l n (x) l n (4)} \frac{2 ln ( 2 )}{x}

簡素化

e^{l n (x) l n (4)} \frac{2 ln ( 2 )}{x} : 2 ln (2) x^{2 l n (2) - 1}

= 2 ln (2) x^{2 l n (2) - 1}