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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

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

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

\int \frac{1}{t + 2} d t

\int_{- 1}^{2} x^{2} e^{x^{3} + 1} d x

f (x) = ln (sec (x))