derivative of (e^{6x}/(x^2+5))

解

\frac{d}{d x} (\frac{e ^{6 x}}{x ^{2} + 5})

\frac{e ^{6 x} \cdot 6 ( x ^{2} + 5 ) - 2 x e ^{6 x}}{( x ^{2} + 5 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{e ^{6 x}}{x ^{2} + 5})

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 ^{6 x} ) ( x ^{2} + 5 ) - \frac{d}{d x} ( x ^{2} + 5 ) e ^{6 x}}{( x ^{2} + 5 ) ^{2}}

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

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

= \frac{e ^{6 x} \cdot 6 ( x ^{2} + 5 ) - 2 x e ^{6 x}}{( x ^{2} + 5 ) ^{2}}