derivative y=(4x-1)/(2x+5)

Lösung

ableitung von

y = \frac{4 x - 1}{2 x + 5}

\frac{22}{( 2 x + 5 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x - 1}{2 x + 5})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 4 x - 1 ) ( 2 x + 5 ) - \frac{d}{d x} ( 2 x + 5 ) ( 4 x - 1 )}{( 2 x + 5 ) ^{2}}

\frac{d}{d x} (4 x - 1) = 4

\frac{d}{d x} (2 x + 5) = 2

= \frac{4 ( 2 x + 5 ) - 2 ( 4 x - 1 )}{( 2 x + 5 ) ^{2}}

Multipliziere aus

4 (2 x + 5) - 2 (4 x - 1) : 22

= \frac{22}{( 2 x + 5 ) ^{2}}

\frac{d}{d x} (sin (x^{3}) cos (x^{2}))

\frac{d y}{d x} = x^{2} - y - 2, y (0) = - 1

\int_{0}^{5} 9800 π (5 - y) d y

\int (sin (x) cos^{3} (x)) d x

x \to \infty lim (\frac{( 2 x - 1 ) ( 3 - x )}{( x - 1 ) ( x + 3 )})