derivative of (x+1/(2x+5))

Lösung

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

\frac{3}{( 2 x + 5 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (2 x + 5) = 2

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

Vereinfache

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

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

x \to 0 + lim (\frac{( 36 - 4 x ^{2} )}{x})

\frac{d}{d x} (10 sec^{2} (x))

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