derivative g(x)=(6x^2)/(2-x)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (2 - x) = - 1

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

Vereinfache

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

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

\int sin^{4} (3 x) - cos^{4} (3 x) d x

\int e^{- s t} \cdot sin (t) d t

\frac{d y}{d x} = x e^{2 y}

\frac{d}{d x} ((1 + cos (2 x))^{2})

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