derivative of (3x^2-9x+1/(7x+8))

Lösung

\frac{d}{d x} (\frac{3 x ^{2} - 9 x + 1}{7 x + 8})

\frac{21 x ^{2} + 48 x - 79}{( 7 x + 8 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x ^{2} - 9 x + 1}{7 x + 8})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x ^{2} - 9 x + 1 ) ( 7 x + 8 ) - \frac{d}{d x} ( 7 x + 8 ) ( 3 x ^{2} - 9 x + 1 )}{( 7 x + 8 ) ^{2}}

\frac{d}{d x} (3 x^{2} - 9 x + 1) = 6 x - 9

\frac{d}{d x} (7 x + 8) = 7

= \frac{( 6 x - 9 ) ( 7 x + 8 ) - 7 ( 3 x ^{2} - 9 x + 1 )}{( 7 x + 8 ) ^{2}}

Multipliziere aus

(6 x - 9) (7 x + 8) - 7 (3 x^{2} - 9 x + 1) : 21 x^{2} + 48 x - 79

= \frac{21 x ^{2} + 48 x - 79}{( 7 x + 8 ) ^{2}}