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

Lösung

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

\frac{12 x ^{2} + 2 x - 4}{x x}

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (8 x^{2} + 4 x + 8) = 16 x + 4

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

= \frac{( 16 x + 4 ) x - \frac{1}{2 x} ( 8 x ^{2} + 4 x + 8 )}{( x ) ^{2}}

Vereinfache

\frac{( 16 x + 4 ) x - \frac{1}{2 x} ( 8 x ^{2} + 4 x + 8 )}{( x ) ^{2}} : \frac{12 x ^{2} + 2 x - 4}{x x}

= \frac{12 x ^{2} + 2 x - 4}{x x}

t an g e n t 4 x^{3}, at x = 1

t an g e n t f (x) = 5 - 3 x, at x = \frac{1}{3}

d er i v a t i v e tan (x)

d er i v a t i v e f (x) = \frac{5}{r ^{3}}

in v erse l a pl a ce \frac{20}{s ( s ^{2} + 4 s + 4 )}