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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

\int ln (4 - x) d x

\frac{d f ^{- 1}}{d x} f (x) = 3 x^{3} - 5 x^{2} - 2, x = 1272

d er i v a t i v e \frac{1 + x}{1 + e ^{x}}

a re a x = 8 y^{2}, x = 20 + 3 y^{2}

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