derivative of ((x+1(2x-3))/(2x+3))

Lösung

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

\frac{4 x ^{2} + 12 x + 3}{( 2 x + 3 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} ((x + 1) (2 x - 3)) = 4 x - 1

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

= \frac{( 4 x - 1 ) ( 2 x + 3 ) - 2 ( x + 1 ) ( 2 x - 3 )}{( 2 x + 3 ) ^{2}}

Multipliziere aus

(4 x - 1) (2 x + 3) - 2 (x + 1) (2 x - 3) : 4 x^{2} + 12 x + 3

= \frac{4 x ^{2} + 12 x + 3}{( 2 x + 3 ) ^{2}}

\int cos^{3} (\frac{x}{9}) d x

\int sin^{4} (z)

d er i v a t i v e y = \frac{x}{1 - 5 x}

\frac{d}{d x} ((- 25 x^{2} + 9)^{2})

d er i v a t i v e 9 cos (4 x)