derivative f(x)=4^{c/x}

解

導関数

f (x) = 4^{\frac{c}{x}}

- \frac{ln ( 2 ) \cdot 2 ^{\frac{x + 2 c}{x}} c}{x ^{2}}

解答ステップ

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

指数の規則を適用する:

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

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= - \frac{ln ( 2 ) \cdot 2 ^{\frac{x + 2 c}{x}} c}{x ^{2}}