derivative (8x+1)/(sqrt(x))

Lösung

ableitung von

\frac{8 x + 1}{x}

\frac{8 x - 1}{2 x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{8 x + 1}{x})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (8 x + 1) = 8

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

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

Vereinfache

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

= \frac{8 x - 1}{2 x x}

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

a re a f (x) = 3 + 2 x - x^{2}, g (x) = x^{2} - 4 x + 3

a re a y = x, y = \frac{1}{4} x, x = 25

t an g e n t f (x) = - x^{3}

\frac{\partial}{\partial y} (\frac{1}{2} sin (2 x - y))