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

Lösung

ableitung von

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

\frac{6 x ^{2} + x - 1}{x x}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (x^{2} - 7 x + 2)

\frac{d}{d x} (3 e^{x} + 5 x^{2})

3 \cdot \frac{d y}{d x} + 5 y = 1

d er i v a t i v e - cos (2 x) - 2 sin (2 x) (1 - x)

a re a 1, 8, [- 0.5 x + 6], x + 2