de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{12 x ^{2} + 4 x - 4}{x x}

Schritte zur Lösung

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

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

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

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

Vereinfache

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

= \frac{12 x ^{2} + 4 x - 4}{x x}

Graph

Beliebte Beispiele

derivative of x^3sinh^2(x+cosh^2(x^3))

fläche x=9,x=y^2

integral of 12x+12

integral of (e^{4x}+4e^x+8)/(e^x)

integral of x^5e^{-x}