derivative of (x^2/(2x+1))

Lösung

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

\frac{2 x ^{2} + 2 x}{( 2 x + 1 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Multipliziere aus

2 x (2 x + 1) - 2 x^{2} : 2 x^{2} + 2 x

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

3 y^{^{''}} + 13 y^{^{'}} + 4 y = 0

\int \frac{1}{x ^{3} - x ^{2}} d x

\frac{d}{d x} (\frac{4}{3 x})

d er i v a t i v e f (x) = - x + \frac{6}{x} + 1

in v erse l a pl a ce \frac{s - 1}{s ^{2} - 2 s + 5}