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

Lösung

ableitung von

\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}}

y^{^{'}} = (2 t + 1) e^{y}

\frac{d}{d z} (z + 1 - 1)

\frac{d}{d x} (3 - \frac{10}{3 x ^{\frac{1}{6}}})

\int \frac{4}{5} sec (x) tan (x) d x

d er i v a t i v e sin (6 θ)