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

Lösung

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

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

Schritte zur Lösung

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

\frac{d}{d x} (6 x^{2} + 6 x + 4) = 12 x + 6

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

= \frac{( 12 x + 6 ) x - \frac{1}{2 x} ( 6 x ^{2} + 6 x + 4 )}{( x ) ^{2}}

Vereinfache

\frac{( 12 x + 6 ) x - \frac{1}{2 x} ( 6 x ^{2} + 6 x + 4 )}{( x ) ^{2}} : \frac{9 x ^{2} + 3 x - 2}{x x}

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

in v erse l a pl a ce \frac{6 s - 4}{s ^{2} - 4 s + 20}

x \to 0 lim (x cos (\frac{1}{x ^{3}}))

y^{^{'}} + x y = x^{3}

d er i v a t i v e (2 x - 1) e^{x}

d er i v a t i v e ln (3 x + 7)