derivative of 656112^{sqrt(x)}

解

\frac{d}{d x} (65611 2^{x})

\frac{ln ( 656112 ) \cdot 4100 7 ^{x} \cdot 2 ^{4 x - 1}}{x}

解答ステップ

\frac{d}{d x} (65611 2^{x})

指数の規則を適用する:

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

65611 2^{x} = e^{x l n (656112)}

= \frac{d}{d x} (e^{x l n (656112)})

連鎖法則を適用:

e^{x l n (656112)} \frac{d}{d x} (x ln (656112))

= e^{x l n (656112)} \frac{d}{d x} (x ln (656112))

\frac{d}{d x} (x ln (656112)) = \frac{ln ( 656112 )}{2 x}

= e^{x l n (656112)} \frac{ln ( 656112 )}{2 x}

簡素化

e^{x l n (656112)} \frac{ln ( 656112 )}{2 x} : \frac{ln ( 656112 ) \cdot 4100 7 ^{x} \cdot 2 ^{4 x - 1}}{x}

= \frac{ln ( 656112 ) \cdot 4100 7 ^{x} \cdot 2 ^{4 x - 1}}{x}