derivative f(x)=(5^x)/x

解

導関数

f (x) = \frac{5 ^{x}}{x}

\frac{ln ( 5 ) \cdot 5 ^{x} x - 5 ^{x}}{x ^{2}}

解答ステップ

\frac{d}{d x} (\frac{5 ^{x}}{x})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 5 ^{x} ) x - \frac{d x}{d x} 5 ^{x}}{x ^{2}}

\frac{d}{d x} (5^{x}) = 5^{x} ln (5)

\frac{d x}{d x} = 1

= \frac{5 ^{x} ln ( 5 ) x - 1 \cdot 5 ^{x}}{x ^{2}}

簡素化

= \frac{ln ( 5 ) \cdot 5 ^{x} x - 5 ^{x}}{x ^{2}}