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Beliebt Rechnen >

derivative of (8x^2+6x+4/(sqrt(x)))

Lösung

\frac{d}{d x} (\frac{8 x ^{2} + 6 x + 4}{x})

Lösung

\frac{12 x ^{2} + 3 x - 2}{x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{8 x ^{2} + 6 x + 4}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 8 x ^{2} + 6 x + 4 ) x - \frac{d}{d x} ( x ) ( 8 x ^{2} + 6 x + 4 )}{( x ) ^{2}}

\frac{d}{d x} (8 x^{2} + 6 x + 4) = 16 x + 6

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

= \frac{( 16 x + 6 ) x - \frac{1}{2 x} ( 8 x ^{2} + 6 x + 4 )}{( x ) ^{2}}

Vereinfache

\frac{( 16 x + 6 ) x - \frac{1}{2 x} ( 8 x ^{2} + 6 x + 4 )}{( x ) ^{2}} : \frac{12 x ^{2} + 3 x - 2}{x x}

= \frac{12 x ^{2} + 3 x - 2}{x x}

Graph

Beliebte Beispiele

(d^2)/(dx^2)(5sec(x))

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

derivative f(x)=6e^{x^{-5}}

d er i v a t i v e f (x) = 6 e^{x^{- 5}}

2 y d x + 3 x d y = 0

integral of e^{2x}2

\int e^{2 x} 2 d x

normal y=x^2-3x,(5,10)

n or ma l y = x^{2} - 3 x, (5, 10)