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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Multipliziere aus

(2 x e^{x} + e^{x} x^{2}) (x^{2} + e^{x}) - (2 x + e^{x}) x^{2} e^{x} : e^{x} x^{4} + 2 e^{2 x} x

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

y^{^{''}} - 4 y^{^{'}} + 4 y^{^{'}} = 0

\int cos^{3} (\frac{x}{12}) d x

x \to 4 + lim (\frac{x - 4}{x - 4})

t an g e n t 2 x^{2} - 9 x + 10

\int_{0}^{3} 1