derivative y=(5x-2)/(sqrt(x))

Lösung

ableitung von

y = \frac{5 x - 2}{x}

\frac{5 x + 2}{2 x x}

Schritte zur Lösung

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

\frac{d}{d x} (5 x - 2) = 5

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

= \frac{5 x - \frac{1}{2 x} ( 5 x - 2 )}{( x ) ^{2}}

Vereinfache

\frac{5 x - \frac{1}{2 x} ( 5 x - 2 )}{( x ) ^{2}} : \frac{5 x + 2}{2 x x}

= \frac{5 x + 2}{2 x x}

t an g e n t 8 x^{- 2}

\int - x d x

x \to 0 lim (arccot (\frac{1}{x}))

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

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