derivative y=(4x^2+8x+4)/(sqrt(x))

Lösung

ableitung von

y = \frac{4 x ^{2} + 8 x + 4}{x}

\frac{6 x ^{2} + 4 x - 2}{x x}

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

x \to 5 lim (5 - x)

k = 0 \sum \infty \frac{1}{2} \cdot (- 1)^{k}

\frac{\partial}{\partial x} (\frac{1}{1 + x ^{2}})

x \to 1 lim (1^{\frac{1}{1 - x}})

\frac{\partial}{\partial u} (u + v w)