derivative of (e^x/(-8x^7))

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

\frac{e ^{x}}{- 8 x ^{7}} : - \frac{e ^{x}}{8 x ^{7}}

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

Entferne die Konstante:

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

= - \frac{1}{8} \frac{d}{d x} (\frac{e ^{x}}{x ^{7}})

Wende die Quotientenregel an:

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

= - \frac{1}{8} \cdot \frac{\frac{d}{d x} ( e ^{x} ) x ^{7} - \frac{d}{d x} ( x ^{7} ) e ^{x}}{( x ^{7} ) ^{2}}

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

\frac{d}{d x} (x^{7}) = 7 x^{6}

= - \frac{1}{8} \cdot \frac{e ^{x} x ^{7} - 7 x ^{6} e ^{x}}{( x ^{7} ) ^{2}}

Vereinfache

- \frac{1}{8} \cdot \frac{e ^{x} x ^{7} - 7 x ^{6} e ^{x}}{( x ^{7} ) ^{2}} : - \frac{e ^{x} ( x - 7 )}{8 x ^{8}}

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

x \to - \infty lim (5 x^{5} - 7 x^{4} + 1)

x cos^{2} (y) d x + tan (y) d y = 0

s l o p e in t erce pt (1.1) (0.1)

\frac{d}{d x} (tan (2 x^{5}))

\int \frac{2 x}{x ^{2} - x - 2} d x