derivative (x-1)/(x^2)

Lösung

ableitung von

\frac{x - 1}{x ^{2}}

\frac{- x + 2}{x ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{- x + 2}{x ^{3}}

x \to 0 + lim (tan (\frac{1}{x}))

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