derivative f(x)=(1+sqrt(3x))/(1-sqrt(3x))

Lösung

ableitung von

f (x) = \frac{1 + 3 x}{1 - 3 x}

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int \frac{x ^{3}}{x ^{2} - 9} d x

t a y l or sin (2 x), 0

\frac{d}{d t} (\frac{e ^{- t}}{1 + t ^{2}})

d er i v a t i v e arcsec (x) \cdot arccos (x)

\int t e^{t + 2} d t