derivative of ((x^2-5x^2)/((6x+7)^3))

Lösung

\frac{d}{d x} (\frac{( x ^{2} - 5 x ) ^{2}}{( 6 x + 7 ) ^{3}})

\frac{2 ( x ^{2} - 5 x ) ( 3 x ^{2} + 29 x - 35 )}{( 6 x + 7 ) ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( x ^{2} - 5 x ) ^{2}}{( 6 x + 7 ) ^{3}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ( x ^{2} - 5 x ) ^{2} ) ( 6 x + 7 ) ^{3} - \frac{d}{d x} ( ( 6 x + 7 ) ^{3} ) ( x ^{2} - 5 x ) ^{2}}{( ( 6 x + 7 ) ^{3} ) ^{2}}

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

\frac{d}{d x} ((6 x + 7)^{3}) = 18 (6 x + 7)^{2}

= \frac{2 ( x ^{2} - 5 x ) ( 2 x - 5 ) ( 6 x + 7 ) ^{3} - 18 ( 6 x + 7 ) ^{2} ( x ^{2} - 5 x ) ^{2}}{( ( 6 x + 7 ) ^{3} ) ^{2}}

Vereinfache

\frac{2 ( x ^{2} - 5 x ) ( 2 x - 5 ) ( 6 x + 7 ) ^{3} - 18 ( 6 x + 7 ) ^{2} ( x ^{2} - 5 x ) ^{2}}{( ( 6 x + 7 ) ^{3} ) ^{2}} : \frac{2 ( x ^{2} - 5 x ) ( 3 x ^{2} + 29 x - 35 )}{( 6 x + 7 ) ^{4}}

= \frac{2 ( x ^{2} - 5 x ) ( 3 x ^{2} + 29 x - 35 )}{( 6 x + 7 ) ^{4}}

s l o p e (- 5, 5), (- 7, 5)

\frac{d}{d x} (\frac{5 x ^{2} - 15}{3 ( x ^{2} - 5 ) ^{\frac{2}{3}}})

x \to a lim (0^{0})

\int_{- 3}^{2} 1 0^{x} ln (10) d x

\int x^{\frac{- 2}{3}} d x