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Beliebt Rechnen >

derivative ((x^2))/(1+x)

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (1 + x) = 1

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of 6x(4+x^2)^{1/2}

\int 6 x (4 + x^{2})^{\frac{1}{2}} d x

implicit (dy)/(dx),4x^2+5xy-y^2=2

im pl i c i t \frac{d y}{d x}, 4 x^{2} + 5 x y - y^{2} = 2

laplacetransform-3sin(4t)

l a pl a ce t r an s f or m - 3 sin (4 t)

x*(dy)/(dx)-x^2+x*e^{-x}=0

x \cdot \frac{d y}{d x} - x^{2} + x \cdot e^{- x} = 0

derivative of (x^5/5)

\frac{d}{d x} (\frac{x ^{5}}{5})