derivative (sqrt(x))/(6x+2)

Lösung

ableitung von

\frac{x}{6 x + 2}

\frac{- 3 x + 1}{x ( 6 x + 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{\frac{1}{2 x} ( 6 x + 2 ) - 6 x}{( 6 x + 2 ) ^{2}} : \frac{- 3 x + 1}{x ( 6 x + 2 ) ^{2}}

= \frac{- 3 x + 1}{x ( 6 x + 2 ) ^{2}}

d er i v a t i v e \frac{x ^{2}}{x - 1}

\int \frac{1}{1 + 2 x ^{2} + x ^{4}} d x

in v erse l a pl a ce \frac{4 + s}{s ^{2} + 3 s + 1}

\frac{\partial}{\partial x} (2 x^{3} y^{3} + 3 x + 4 y)

d er i v a t i v e \frac{3}{2 x ^{2}} + 2 5 x^{3}