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Beliebt Rechnen >

derivative of (x^2/(7+sqrt(x)))

Lösung

\frac{d}{d x} (\frac{x ^{2}}{7 + x})

Lösung

\frac{4 x ( 7 + x ) - x ^{\frac{3}{2}}}{2 ( 7 + x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{7 + x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 7 + x ) - \frac{d}{d x} ( 7 + x ) x ^{2}}{( 7 + x ) ^{2}}

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

\frac{d}{d x} (7 + x) = \frac{1}{2 x}

= \frac{2 x ( 7 + x ) - \frac{1}{2 x} x ^{2}}{( 7 + x ) ^{2}}

Vereinfache

\frac{2 x ( 7 + x ) - \frac{1}{2 x} x ^{2}}{( 7 + x ) ^{2}} : \frac{4 x ( 7 + x ) - x ^{\frac{3}{2}}}{2 ( 7 + x ) ^{2}}

= \frac{4 x ( 7 + x ) - x ^{\frac{3}{2}}}{2 ( 7 + x ) ^{2}}

Graph

Beliebte Beispiele

integral from-infinity to 0 of 1/(2-4x)

\int_{- \infty}^{0} \frac{1}{2 - 4 x} d x

integral from a to b of f(x)

\int_{a}^{b} f (x) d x

(ln (\frac{x}{4}))^{^{'}}

integral of 2x(2-x)

\int 2 x (2 - x) d x

derivative 3^{2^{x^2}}

d er i v a t i v e 3^{2^{x^{2}}}