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Beliebt Rechnen >

derivative f(x)=(sqrt(x))/(3+x)

Lösung

ableitung von

f (x) = \frac{x}{3 + x}

Lösung

\frac{3 - x}{2 x ( 3 + x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{3 + x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ) ( 3 + x ) - \frac{d}{d x} ( 3 + x ) x}{( 3 + x ) ^{2}}

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

\frac{d}{d x} (3 + x) = 1

= \frac{\frac{1}{2 x} ( 3 + x ) - 1 \cdot x}{( 3 + x ) ^{2}}

Vereinfache

\frac{\frac{1}{2 x} ( 3 + x ) - 1 \cdot x}{( 3 + x ) ^{2}} : \frac{3 - x}{2 x ( 3 + x ) ^{2}}

= \frac{3 - x}{2 x ( 3 + x ) ^{2}}

Graph

Beliebte Beispiele

integral from 0 to pi of cos(x)cos(nx)

\int_{0}^{π} cos (x) cos (n x) d x

(x^3+e^y)(dy)/(dx)=3x^2

(x^{3} + e^{y}) \frac{d y}{d x} = 3 x^{2}

limit as x approaches infinity of x-1

x \to \infty lim (x - 1)

(d^2y)/(dt^2)+2(dy)/(dt)+y=0

\frac{d ^{2} y}{d t ^{2}} + 2 \frac{d y}{d t} + y = 0

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\frac{d}{d x} (\frac{x}{( x - 9 ) ^{2}})