derivative ((8x^3-4x^2+3))/x

Lösung

ableitung von

\frac{( 8 x ^{3} - 4 x ^{2} + 3 )}{x}

\frac{16 x ^{3} - 4 x ^{2} - 3}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{8 x ^{3} - 4 x ^{2} + 3}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 8 x ^{3} - 4 x ^{2} + 3 ) x - \frac{d x}{d x} ( 8 x ^{3} - 4 x ^{2} + 3 )}{x ^{2}}

\frac{d}{d x} (8 x^{3} - 4 x^{2} + 3) = 24 x^{2} - 8 x

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

= \frac{( 24 x ^{2} - 8 x ) x - 1 \cdot ( 8 x ^{3} - 4 x ^{2} + 3 )}{x ^{2}}

Vereinfache

\frac{( 24 x ^{2} - 8 x ) x - 1 \cdot ( 8 x ^{3} - 4 x ^{2} + 3 )}{x ^{2}} : \frac{16 x ^{3} - 4 x ^{2} - 3}{x ^{2}}

= \frac{16 x ^{3} - 4 x ^{2} - 3}{x ^{2}}

x \to - 1 lim (3 x + 1)

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