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Beliebt Rechnen >

derivative y=(6x^2+2x+6)/(sqrt(x))

Lösung

ableitung von

y = \frac{6 x ^{2} + 2 x + 6}{x}

Lösung

\frac{9 x ^{2} + x - 3}{x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{6 x ^{2} + 2 x + 6}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 6 x ^{2} + 2 x + 6 ) x - \frac{d}{d x} ( x ) ( 6 x ^{2} + 2 x + 6 )}{( x ) ^{2}}

\frac{d}{d x} (6 x^{2} + 2 x + 6) = 12 x + 2

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

= \frac{( 12 x + 2 ) x - \frac{1}{2 x} ( 6 x ^{2} + 2 x + 6 )}{( x ) ^{2}}

Vereinfache

\frac{( 12 x + 2 ) x - \frac{1}{2 x} ( 6 x ^{2} + 2 x + 6 )}{( x ) ^{2}} : \frac{9 x ^{2} + x - 3}{x x}

= \frac{9 x ^{2} + x - 3}{x x}

Graph

Beliebte Beispiele

(dy)/(dx)-2xy=10x

\frac{d y}{d x} - 2 x y = 10 x

(\partial)/(\partial x)(3xy)

\frac{\partial}{\partial x} (3 x y)

integral of cos(4x)cos(6x)

\int cos (4 x) cos (6 x) d x

integral of 1/((x^2+R^2)^{3/2)}

\int \frac{1}{( x ^{2} + R ^{2} ) ^{\frac{3}{2}}} d x

2 y + x y^{^{'}} = 0