derivative of (x+7/(x-7))

Lösung

\frac{d}{d x} (\frac{x + 7}{x - 7})

- \frac{14}{( x - 7 ) ^{2}}

Schritte zur Lösung

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

\frac{d}{d x} (x + 7) = 1

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

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

Vereinfache

\frac{1 \cdot ( x - 7 ) - 1 \cdot ( x + 7 )}{( x - 7 ) ^{2}} : - \frac{14}{( x - 7 ) ^{2}}

= - \frac{14}{( x - 7 ) ^{2}}

t an g e n t y = 3 x + 72, (3, 9)

x \to 0 lim (\frac{x ^{2}}{e ^{x} - 1})

\int 3 sec (x) d x

\frac{\partial}{\partial x} (a^{2})

\int (x - 2)^{\frac{3}{2}} d x