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Beliebt Rechnen >

derivative f(x)=((8x+x^2))/((4+x)^2)

Lösung

ableitung von

f (x) = \frac{( 8 x + x ^{2} )}{( 4 + x ) ^{2}}

Lösung

\frac{32}{( 4 + x ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{8 x + x ^{2}}{( 4 + x ) ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 8 x + x ^{2} ) ( 4 + x ) ^{2} - \frac{d}{d x} ( ( 4 + x ) ^{2} ) ( 8 x + x ^{2} )}{( ( 4 + x ) ^{2} ) ^{2}}

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

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

= \frac{( 8 + 2 x ) ( 4 + x ) ^{2} - 2 ( 4 + x ) ( 8 x + x ^{2} )}{( ( 4 + x ) ^{2} ) ^{2}}

Vereinfache

\frac{( 8 + 2 x ) ( 4 + x ) ^{2} - 2 ( 4 + x ) ( 8 x + x ^{2} )}{( ( 4 + x ) ^{2} ) ^{2}} : \frac{32}{( 4 + x ) ^{3}}

= \frac{32}{( 4 + x ) ^{3}}

Graph

Beliebte Beispiele

integral of (3x)/(3x+2)

\int \frac{3 x}{3 x + 2} d x

limit as x approaches 3 of (x^2-25)/(sqrt(x^2+11))

x \to 3 lim (\frac{x ^{2} - 25}{x ^{2} + 11})

integral from 0 to 2 of 2e^{-3x}

\int_{0}^{2} 2 e^{- 3 x} d x

derivative of (x^{1/3}-1^3)

\frac{d}{d x} ((x^{\frac{1}{3}} - 1)^{3})

xy^'=y+3x^2sin(x),y(pi)=0

x y^{^{'}} = y + 3 x^{2} sin (x), y (π) = 0