derivative (e^x)/(x^2+14)

Lösung

ableitung von

\frac{e ^{x}}{x ^{2} + 14}

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

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{x}}{x ^{2} + 14})

Wende die Quotientenregel an:

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

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

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

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

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

\int_{1}^{2} \frac{7}{x ^{3} + 4 x} d x

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