derivative of (6x-3/(5x+8))

Lösung

\frac{d}{d x} (\frac{6 x - 3}{5 x + 8})

\frac{63}{( 5 x + 8 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{6 x - 3}{5 x + 8})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 6 x - 3 ) ( 5 x + 8 ) - \frac{d}{d x} ( 5 x + 8 ) ( 6 x - 3 )}{( 5 x + 8 ) ^{2}}

\frac{d}{d x} (6 x - 3) = 6

\frac{d}{d x} (5 x + 8) = 5

= \frac{6 ( 5 x + 8 ) - 5 ( 6 x - 3 )}{( 5 x + 8 ) ^{2}}

Multipliziere aus

6 (5 x + 8) - 5 (6 x - 3) : 63

= \frac{63}{( 5 x + 8 ) ^{2}}

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