derivative of (e^x/(x^4+1))

解

\frac{d}{d x} (\frac{e ^{x}}{x ^{4} + 1})

\frac{e ^{x} ( x ^{4} + 1 ) - 4 x ^{3} e ^{x}}{( x ^{4} + 1 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{e ^{x}}{x ^{4} + 1})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( x ^{4} + 1 ) - \frac{d}{d x} ( x ^{4} + 1 ) e ^{x}}{( x ^{4} + 1 ) ^{2}}

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (x^{4} + 1) = 4 x^{3}

= \frac{e ^{x} ( x ^{4} + 1 ) - 4 x ^{3} e ^{x}}{( x ^{4} + 1 ) ^{2}}