derivative of (6-7x/(2+x))

Lösung

\frac{d}{d x} (\frac{6 - 7 x}{2 + x})

- \frac{20}{( 2 + x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{6 - 7 x}{2 + x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 6 - 7 x ) ( 2 + x ) - \frac{d}{d x} ( 2 + x ) ( 6 - 7 x )}{( 2 + x ) ^{2}}

\frac{d}{d x} (6 - 7 x) = - 7

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

= \frac{( - 7 ) ( 2 + x ) - 1 \cdot ( 6 - 7 x )}{( 2 + x ) ^{2}}

Vereinfache

\frac{( - 7 ) ( 2 + x ) - 1 \cdot ( 6 - 7 x )}{( 2 + x ) ^{2}} : - \frac{20}{( 2 + x ) ^{2}}

= - \frac{20}{( 2 + x ) ^{2}}

x \to 6 - lim (\frac{x ^{6}}{x - 6})

a re a 5 x, 2 x^{2}

\int x^{\frac{7}{2}} ln (x) d x

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