derivative y=(5x^2+8x+4)/(sqrt(x))

Lösung

ableitung von

y = \frac{5 x ^{2} + 8 x + 4}{x}

\frac{15 x ^{2} + 8 x - 4}{2 x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{5 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} ( 5 x ^{2} + 8 x + 4 ) x - \frac{d}{d x} ( x ) ( 5 x ^{2} + 8 x + 4 )}{( x ) ^{2}}

\frac{d}{d x} (5 x^{2} + 8 x + 4) = 10 x + 8

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

= \frac{( 10 x + 8 ) x - \frac{1}{2 x} ( 5 x ^{2} + 8 x + 4 )}{( x ) ^{2}}

Vereinfache

\frac{( 10 x + 8 ) x - \frac{1}{2 x} ( 5 x ^{2} + 8 x + 4 )}{( x ) ^{2}} : \frac{15 x ^{2} + 8 x - 4}{2 x x}

= \frac{15 x ^{2} + 8 x - 4}{2 x x}

x \to 2 lim (x^{2} + 5)

d er i v a t i v e (4 x)^{2 x}

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

\int x 3^{x} d x

\frac{d}{d x} (\frac{csc ( x )}{cot ( x )})