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

Lösung

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

\frac{3 x ^{2} + 3 x - 1}{x x}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{3 x ^{2} + 3 x - 1}{x x}

x \to 3 - lim (k (x) (x - 5))

\frac{\partial}{\partial z} (e^{x y} + ln (2 x z) + sin (x^{2} y^{2}))

\frac{d}{d x} (\frac{x g ( x ) ( x ) ^{x - 1}}{x ^{2} + 1})

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

\frac{d}{d x} (2 ln (x) - \frac{x ^{2}}{16})