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

Lösung

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

\frac{3 x ^{2} + x - 4}{x x}

Schritte zur Lösung

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

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

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

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

Vereinfache

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

= \frac{3 x ^{2} + x - 4}{x x}

d er i v a t i v e f (x) = lo g_{2} (x)

x \to - 3 - lim (f (x))

\int 2 x + sin (x) + c d x

\frac{\partial}{\partial x} (x^{4} + x^{2} y)

\int \frac{441 - x ^{2}}{x} d x