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

Lösung

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

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

Schritte zur Lösung

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

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

Vereinfache

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

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

d er i v a t i v e f (x) = (2 e^{x} - 3 x^{5})

\int \frac{1}{4 t ^{2} - 4 t + 5} d t

\frac{\partial}{\partial x} (- 4 y^{3} sin (4 x))

\frac{d}{d x} (sin (x) - csc (x))

x \to 2 lim (\frac{x}{x - 2})