derivative f(x)=(3x-9)/(x+5)

Lösung

ableitung von

f (x) = \frac{3 x - 9}{x + 5}

\frac{24}{( x + 5 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x - 9}{x + 5})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x - 9 ) ( x + 5 ) - \frac{d}{d x} ( x + 5 ) ( 3 x - 9 )}{( x + 5 ) ^{2}}

\frac{d}{d x} (3 x - 9) = 3

\frac{d}{d x} (x + 5) = 1

= \frac{3 ( x + 5 ) - 1 \cdot ( 3 x - 9 )}{( x + 5 ) ^{2}}

Vereinfache

\frac{3 ( x + 5 ) - 1 \cdot ( 3 x - 9 )}{( x + 5 ) ^{2}} : \frac{24}{( x + 5 ) ^{2}}

= \frac{24}{( x + 5 ) ^{2}}

n = 1 \sum \infty (0.01)^{n}

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