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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (ln (\frac{7 + e ^{x}}{7 - e ^{x}}))

\int_{0}^{5} \frac{1}{x ^{\frac{13}{12}}} d x

\frac{d}{d x} (3 tan^{2} (x))

\frac{d}{d x} (lo g_{n} (x))

t^{2} \frac{d y}{d t} + y^{2} = t y