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

Lösung

ableitung von

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

\frac{x ^{2} + 4}{x ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{x ^{2} + 4}{x ^{2}}

\int 1 + \frac{1}{4} sin^{2} (x) d x

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