derivative (x^2)/(x+5)

Lösung

ableitung von

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

\frac{x ^{2} + 10 x}{( x + 5 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{x + 5})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( x + 5 ) - \frac{d}{d x} ( x + 5 ) x ^{2}}{( x + 5 ) ^{2}}

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

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

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

Vereinfache

\frac{2 x ( x + 5 ) - 1 \cdot x ^{2}}{( x + 5 ) ^{2}} : \frac{x ^{2} + 10 x}{( x + 5 ) ^{2}}

= \frac{x ^{2} + 10 x}{( x + 5 ) ^{2}}

a re a 1 - 2 x^{2}, ∣ x ∣

t a y l or \frac{1}{1 - x}, 7

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