derivative of (3x+5/(1+x))

Lösung

\frac{d}{d x} (\frac{3 x + 5}{1 + x})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x + 5}{1 + x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x + 5 ) ( 1 + x ) - \frac{d}{d x} ( 1 + x ) ( 3 x + 5 )}{( 1 + x ) ^{2}}

\frac{d}{d x} (3 x + 5) = 3

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

= \frac{3 ( 1 + x ) - 1 \cdot ( 3 x + 5 )}{( 1 + x ) ^{2}}

Vereinfache

\frac{3 ( 1 + x ) - 1 \cdot ( 3 x + 5 )}{( 1 + x ) ^{2}} : - \frac{2}{( 1 + x ) ^{2}}

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

\frac{d}{d x} (3^{x} \cdot ln (3))

\int_{4}^{\infty} e^{- \frac{x}{5}} d x

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