derivative y=(5x^2+4)/(x+3)

Lösung

ableitung von

y = \frac{5 x ^{2} + 4}{x + 3}

\frac{5 x ^{2} + 30 x - 4}{( x + 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5 x ^{2} + 4}{x + 3})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 5 x ^{2} + 4 ) ( x + 3 ) - \frac{d}{d x} ( x + 3 ) ( 5 x ^{2} + 4 )}{( x + 3 ) ^{2}}

\frac{d}{d x} (5 x^{2} + 4) = 10 x

\frac{d}{d x} (x + 3) = 1

= \frac{10 x ( x + 3 ) - 1 \cdot ( 5 x ^{2} + 4 )}{( x + 3 ) ^{2}}

Vereinfache

\frac{10 x ( x + 3 ) - 1 \cdot ( 5 x ^{2} + 4 )}{( x + 3 ) ^{2}} : \frac{5 x ^{2} + 30 x - 4}{( x + 3 ) ^{2}}

= \frac{5 x ^{2} + 30 x - 4}{( x + 3 ) ^{2}}

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