derivative y=(3x-2)/(2x+1)

Lösung

ableitung von

y = \frac{3 x - 2}{2 x + 1}

\frac{7}{( 2 x + 1 ) ^{2}}

Schritte zur Lösung

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

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

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

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

Multipliziere aus

3 (2 x + 1) - 2 (3 x - 2) : 7

= \frac{7}{( 2 x + 1 ) ^{2}}

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

\int \frac{x ^{3}}{( x ^{2} + a ^{2} ) ^{3}} d x

a re a y = 3 x, x + y = 4, y = 1

\int_{- 1}^{1} \frac{5 r}{( 4 + r ^{2} ) ^{2}} d r

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