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Beliebt Rechnen >

derivative of x/(sqrt(x^2+4))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d x}{d x} = 1

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

= \frac{1 \cdot x ^{2} + 4 - \frac{x}{x ^{2} + 4} x}{( x ^{2} + 4 ) ^{2}}

Vereinfache

\frac{1 \cdot x ^{2} + 4 - \frac{x}{x ^{2} + 4} x}{( x ^{2} + 4 ) ^{2}} : \frac{4}{( x ^{2} + 4 ) x ^{2} + 4}

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

Graph

Beliebte Beispiele

limit as x approaches 25 of log_{5}(x)

x \to 25 lim (lo g_{5} (x))

derivative of x^5ln(2x)

\frac{d}{d x} (x^{5} ln (2 x))

derivative f(x)=((x^2)/(x-1))^2

d er i v a t i v e f (x) = (\frac{x ^{2}}{x - 1})^{2}

integral from 0 to 1 of 1

\int_{0}^{1} 1 d x

integral of e^{-4}

\int e^{- 4}