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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{6 x ^{2} + x - 1}{x x}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (4 x^{2} + 2 x + 2) = 8 x + 2

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

= \frac{( 8 x + 2 ) x - \frac{1}{2 x} ( 4 x ^{2} + 2 x + 2 )}{( x ) ^{2}}

Vereinfache

\frac{( 8 x + 2 ) x - \frac{1}{2 x} ( 4 x ^{2} + 2 x + 2 )}{( x ) ^{2}} : \frac{6 x ^{2} + x - 1}{x x}

= \frac{6 x ^{2} + x - 1}{x x}

Graph

Beliebte Beispiele

integral of 1+tan^2(x)

\int 1 + tan^{2} (x) d x

integral from 1 to e of ln(2x)

\int_{1}^{e} ln (2 x) d x

6 y^{^{''}} + y^{^{'}} = 0

derivative of pi/2

\frac{d}{d x} (\frac{π}{2})

integral of 5e^{-4x+8}-5

\int 5 e^{- 4 x + 8} - 5 d x