derivative (x^7+2)/(x^7)

Lösung

ableitung von

\frac{x ^{7} + 2}{x ^{7}}

- \frac{14}{x ^{8}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x^{7} + 2) = 7 x^{6}

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

= \frac{7 x ^{6} x ^{7} - 7 x ^{6} ( x ^{7} + 2 )}{( x ^{7} ) ^{2}}

Vereinfache

\frac{7 x ^{6} x ^{7} - 7 x ^{6} ( x ^{7} + 2 )}{( x ^{7} ) ^{2}} : - \frac{14}{x ^{8}}

= - \frac{14}{x ^{8}}

t an g e n t 11 - x^{2} (3.2)

\int tan^{4} (6 x) sec^{2} (6 x) d x

\frac{\partial}{\partial y} (y^{2} - 9)

\frac{d y}{d x} = - \frac{4 x + 4 y}{4 x + 9 y}

x \to 2 + lim (\frac{x - 3}{x ^{2} - 4})