derivative of (e^xx-e^x/(7x^2))

Lösung

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

\frac{e ^{x} ( x ^{2} - 2 ( x - 1 ) )}{7 x ^{3}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{7} \frac{d}{d x} (\frac{e ^{x} x - e ^{x}}{x ^{2}})

Wende die Quotientenregel an:

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

= \frac{1}{7} \cdot \frac{\frac{d}{d x} ( e ^{x} x - e ^{x} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( e ^{x} x - e ^{x} )}{( x ^{2} ) ^{2}}

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

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

= \frac{1}{7} \cdot \frac{e ^{x} x x ^{2} - 2 x ( e ^{x} x - e ^{x} )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{1}{7} \cdot \frac{e ^{x} x x ^{2} - 2 x ( e ^{x} x - e ^{x} )}{( x ^{2} ) ^{2}} : \frac{e ^{x} ( x ^{2} - 2 ( x - 1 ) )}{7 x ^{3}}

= \frac{e ^{x} ( x ^{2} - 2 ( x - 1 ) )}{7 x ^{3}}

\frac{\partial}{\partial y} (sin (x - y) + (x - y))

\frac{d}{d x} (x - 3 e^{x})

\frac{\partial}{\partial x} (ln (x^{2} + 3))

x \to 2 lim (\frac{2 x - 4}{x - 2})

(3 x^{2} + y - 4) - (2 y - x) \frac{d y}{d x} = 0