derivative of (4x-x^2/(6-x))

Lösung

\frac{d}{d x} (\frac{4 x - x ^{2}}{6 - x})

\frac{x ^{2} - 12 x + 24}{( 6 - x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x - x ^{2}}{6 - x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 4 x - x ^{2} ) ( 6 - x ) - \frac{d}{d x} ( 6 - x ) ( 4 x - x ^{2} )}{( 6 - x ) ^{2}}

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

\frac{d}{d x} (6 - x) = - 1

= \frac{( 4 - 2 x ) ( 6 - x ) - ( - 1 ) ( 4 x - x ^{2} )}{( 6 - x ) ^{2}}

Vereinfache

\frac{( 4 - 2 x ) ( 6 - x ) - ( - 1 ) ( 4 x - x ^{2} )}{( 6 - x ) ^{2}} : \frac{x ^{2} - 12 x + 24}{( 6 - x ) ^{2}}

= \frac{x ^{2} - 12 x + 24}{( 6 - x ) ^{2}}

d er i v a t i v e e^{- x^{4}}

\int \frac{1}{( 8 x + 9 ) ^{2}} d x

n = 1 \sum \infty (- 4)^{n}

\int sec (x) tan (x) - 4 e^{x} d x

\int sinh (4 x) d x