derivative f(x)=(4x)/((x-1)^2)

Lösung

ableitung von

f (x) = \frac{4 x}{( x - 1 ) ^{2}}

\frac{4 ( - 1 - x )}{( x - 1 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x}{( x - 1 ) ^{2}})

Entferne die Konstante:

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

= 4 \frac{d}{d x} (\frac{x}{( x - 1 ) ^{2}})

Wende die Quotientenregel an:

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

= 4 \cdot \frac{\frac{d x}{d x} ( x - 1 ) ^{2} - \frac{d}{d x} ( ( x - 1 ) ^{2} ) x}{( ( x - 1 ) ^{2} ) ^{2}}

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

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

= 4 \cdot \frac{1 \cdot ( x - 1 ) ^{2} - 2 ( x - 1 ) x}{( ( x - 1 ) ^{2} ) ^{2}}

Vereinfache

4 \cdot \frac{1 \cdot ( x - 1 ) ^{2} - 2 ( x - 1 ) x}{( ( x - 1 ) ^{2} ) ^{2}} : \frac{4 ( - 1 - x )}{( x - 1 ) ^{3}}

= \frac{4 ( - 1 - x )}{( x - 1 ) ^{3}}

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