derivative f(x)=(x+6)/(x-6)

Lösung

ableitung von

f (x) = \frac{x + 6}{x - 6}

- \frac{12}{( x - 6 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x + 6}{x - 6})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x + 6) = 1

\frac{d}{d x} (x - 6) = 1

= \frac{1 \cdot ( x - 6 ) - 1 \cdot ( x + 6 )}{( x - 6 ) ^{2}}

Vereinfache

\frac{1 \cdot ( x - 6 ) - 1 \cdot ( x + 6 )}{( x - 6 ) ^{2}} : - \frac{12}{( x - 6 ) ^{2}}

= - \frac{12}{( x - 6 ) ^{2}}

t a y l or (1 - x) e^{x + \frac{x ^{2}}{2}}

x \to 0 + lim (- x^{2} ln (6 x^{3}))

\int \frac{6}{5 + 6 x} d x

\int e^{x} 2 d x

\frac{\partial}{\partial x} (6 e^{x y + 5})