derivative of (14x+8x^2/((7+8x)^2))

Lösung

\frac{d}{d x} (\frac{14 x + 8 x ^{2}}{( 7 + 8 x ) ^{2}})

\frac{98}{( 7 + 8 x ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{14 x + 8 x ^{2}}{( 7 + 8 x ) ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 14 x + 8 x ^{2} ) ( 7 + 8 x ) ^{2} - \frac{d}{d x} ( ( 7 + 8 x ) ^{2} ) ( 14 x + 8 x ^{2} )}{( ( 7 + 8 x ) ^{2} ) ^{2}}

\frac{d}{d x} (14 x + 8 x^{2}) = 14 + 16 x

\frac{d}{d x} ((7 + 8 x)^{2}) = 16 (7 + 8 x)

= \frac{( 14 + 16 x ) ( 7 + 8 x ) ^{2} - 16 ( 7 + 8 x ) ( 14 x + 8 x ^{2} )}{( ( 7 + 8 x ) ^{2} ) ^{2}}

Vereinfache

\frac{( 14 + 16 x ) ( 7 + 8 x ) ^{2} - 16 ( 7 + 8 x ) ( 14 x + 8 x ^{2} )}{( ( 7 + 8 x ) ^{2} ) ^{2}} : \frac{98}{( 7 + 8 x ) ^{3}}

= \frac{98}{( 7 + 8 x ) ^{3}}

\int 5 e^{x} + 3 sin (x) d x

\int \frac{1}{x 4 x ^{2} + 49} d x

\frac{d}{d x} (- 27 e^{- 3 x})

\frac{d}{d x} (e^{- 0.01 x})

\int 12 t d t