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Beliebt Rechnen >

derivative of (x^2/(8-8x))

Lösung

\frac{d}{d x} (\frac{x ^{2}}{8 - 8 x})

Lösung

\frac{x ( - x + 2 )}{8 ( x - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{8 - 8 x})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (8 - 8 x) = - 8

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

Vereinfache

\frac{2 x ( 8 - 8 x ) - ( - 8 ) x ^{2}}{( 8 - 8 x ) ^{2}} : \frac{x ( - x + 2 )}{8 ( x - 1 ) ^{2}}

= \frac{x ( - x + 2 )}{8 ( x - 1 ) ^{2}}

Graph

Beliebte Beispiele

limit as x approaches 0 of sin(x)+cos(x)

x \to 0 lim (sin (x) + cos (x))

derivative y=(x^3+8)/x

d er i v a t i v e y = \frac{x ^{3} + 8}{x}

f (u) = \frac{1}{u}

derivative g(x)=tan(2x)*sin(2x)

d er i v a t i v e g (x) = tan (2 x) \cdot sin (2 x)

derivative y=sqrt(2x-x^2)

d er i v a t i v e y = 2 x - x^{2}