derivative of ((7x-1(x+5))/(36x))

Lösung

\frac{d}{d x} (\frac{( 7 x - 1 ) ( x + 5 )}{36 x})

\frac{7 x ^{2} + 5}{36 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( 7 x - 1 ) ( x + 5 )}{36 x})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{36} \frac{d}{d x} (\frac{( 7 x - 1 ) ( x + 5 )}{x})

Wende die Quotientenregel an:

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

= \frac{1}{36} \cdot \frac{\frac{d}{d x} ( ( 7 x - 1 ) ( x + 5 ) ) x - \frac{d x}{d x} ( 7 x - 1 ) ( x + 5 )}{x ^{2}}

\frac{d}{d x} ((7 x - 1) (x + 5)) = 14 x + 34

\frac{d x}{d x} = 1

= \frac{1}{36} \cdot \frac{( 14 x + 34 ) x - 1 \cdot ( 7 x - 1 ) ( x + 5 )}{x ^{2}}

Vereinfache

\frac{1}{36} \cdot \frac{( 14 x + 34 ) x - 1 \cdot ( 7 x - 1 ) ( x + 5 )}{x ^{2}} : \frac{7 x ^{2} + 5}{36 x ^{2}}

= \frac{7 x ^{2} + 5}{36 x ^{2}}

x \to 0 lim (3 - \frac{4}{x})

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