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

Lösung

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

\frac{x ^{2} - 8 x + 12}{( 3 x - x ^{2} ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x - 4) = 1

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

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

Vereinfache

\frac{1 \cdot ( 3 x - x ^{2} ) - ( 3 - 2 x ) ( x - 4 )}{( 3 x - x ^{2} ) ^{2}} : \frac{x ^{2} - 8 x + 12}{( 3 x - x ^{2} ) ^{2}}

= \frac{x ^{2} - 8 x + 12}{( 3 x - x ^{2} ) ^{2}}

\int 2 + 2 cos (x) d x

a re a y = 2 x^{2}, y = 8 x^{2}, 5 x + y = 3

\frac{d}{d x} (2 e^{x} + x e^{x})

\int_{7}^{9} \frac{7}{( x - 8 ) ^{10}} d x

n = 1 \sum \infty \frac{1}{2} (0.3)^{n}