derivative of (6x^2+2x+8/(sqrt(x)))

Lösung

\frac{d}{d x} (\frac{6 x ^{2} + 2 x + 8}{x})

\frac{9 x ^{2} + x - 4}{x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{6 x ^{2} + 2 x + 8}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 6 x ^{2} + 2 x + 8 ) x - \frac{d}{d x} ( x ) ( 6 x ^{2} + 2 x + 8 )}{( x ) ^{2}}

\frac{d}{d x} (6 x^{2} + 2 x + 8) = 12 x + 2

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

= \frac{( 12 x + 2 ) x - \frac{1}{2 x} ( 6 x ^{2} + 2 x + 8 )}{( x ) ^{2}}

Vereinfache

\frac{( 12 x + 2 ) x - \frac{1}{2 x} ( 6 x ^{2} + 2 x + 8 )}{( x ) ^{2}} : \frac{9 x ^{2} + x - 4}{x x}

= \frac{9 x ^{2} + x - 4}{x x}

t an g e n t y = 3 x^{3} - x^{2} + 8, (2, 28)

\int (t^{2} - 2 cos (t)) d t

d er i v a t i v e f (x) = 2 x^{2} - 3 x + 1

x \to 0 lim (\frac{100}{x ^{2}})

d er i v a t i v e cos^{3} (t)