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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{- cos ( x ) - 1}{x ^{3} + x ^{2}})

t an g e n t y = 1 + 4 x^{2} - 2 x^{3}

\frac{\partial}{\partial y} (x^{3} - x y^{2} + 3 y^{2})

t an g e n t y = 4 x^{3} - 2 x, (1, 2)

t an g e n t f (x) = x^{2} + 1, (- 4, 17)