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

Lösung

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

\frac{9 x ^{2} + 4 x - 2}{x x}

Schritte zur Lösung

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

\frac{d}{d x} (6 x^{2} + 8 x + 4) = 12 x + 8

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

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

Vereinfache

\frac{( 12 x + 8 ) x - \frac{1}{2 x} ( 6 x ^{2} + 8 x + 4 )}{( x ) ^{2}} : \frac{9 x ^{2} + 4 x - 2}{x x}

= \frac{9 x ^{2} + 4 x - 2}{x x}

\frac{d}{d x} ((x)^{x + 1})

\frac{d x}{d y} = sin (x + y)

y^{^{'}} = - a y

\frac{d}{d x} (x^{a} y^{1 - a})

s l o p e (1, - 1), (6, - 1)