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

Lösung

ableitung von

\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 0 lim (\frac{( x ^{3} )}{x ^{2}})

\frac{d}{d x} (\frac{7 e ^{x} x ^{\frac{5}{2}}}{2} + e^{x} x^{\frac{7}{2}})

\frac{\partial}{\partial x} (x y^{3})

\int_{0}^{1} \frac{x ^{3}}{x ^{2} - x - 6} d x

in v erse l a pl a ce \frac{1}{s ^{2} + 40 s + 2000}