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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int cos^{2} (θ) sin (θ) d θ

\int x e^{(x^{2})} d x

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

x \to 0 - lim (0)

l a pl a ce t r an s f or m 3 t^{5}