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Beliebt Rechnen >

derivative of (sqrt(x)/(2-x))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative of [x+(x+sin^2(x)^3]^6)

\frac{d}{d x} ([x + (x + sin^{2} (x))^{3}]^{6})

derivative of (sec(x)/x)

\frac{d}{d x} (\frac{sec ( x )}{x})

derivative of (ln(3)^x)

\frac{d}{d x} ((ln (3))^{x})

integral of sqrt(x/2)

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

tangent f(x)=3x^2+9x^3-5x,\at x=-4

t an g e n t f (x) = 3 x^{2} + 9 x^{3} - 5 x, at x = - 4