derivative of (3x-4/(x+2))

Lösung

\frac{d}{d x} (\frac{3 x - 4}{x + 2})

\frac{10}{( x + 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x - 4}{x + 2})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x - 4 ) ( x + 2 ) - \frac{d}{d x} ( x + 2 ) ( 3 x - 4 )}{( x + 2 ) ^{2}}

\frac{d}{d x} (3 x - 4) = 3

\frac{d}{d x} (x + 2) = 1

= \frac{3 ( x + 2 ) - 1 \cdot ( 3 x - 4 )}{( x + 2 ) ^{2}}

Vereinfache

\frac{3 ( x + 2 ) - 1 \cdot ( 3 x - 4 )}{( x + 2 ) ^{2}} : \frac{10}{( x + 2 ) ^{2}}

= \frac{10}{( x + 2 ) ^{2}}

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