derivative of (e^x/(7x^2+8))

Lösung

\frac{d}{d x} (\frac{e ^{x}}{7 x ^{2} + 8})

\frac{e ^{x} ( 7 x ^{2} + 8 ) - 14 x e ^{x}}{( 7 x ^{2} + 8 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{x}}{7 x ^{2} + 8})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( 7 x ^{2} + 8 ) - \frac{d}{d x} ( 7 x ^{2} + 8 ) e ^{x}}{( 7 x ^{2} + 8 ) ^{2}}

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

\frac{d}{d x} (7 x^{2} + 8) = 14 x

= \frac{e ^{x} ( 7 x ^{2} + 8 ) - 14 x e ^{x}}{( 7 x ^{2} + 8 ) ^{2}}

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