derivative of (4x^3+2x+5/x)

Lösung

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

\frac{8 x ^{3} - 5}{x ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (4 x^{3} + 2 x + 5) = 12 x^{2} + 2

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

= \frac{( 12 x ^{2} + 2 ) x - 1 \cdot ( 4 x ^{3} + 2 x + 5 )}{x ^{2}}

Vereinfache

\frac{( 12 x ^{2} + 2 ) x - 1 \cdot ( 4 x ^{3} + 2 x + 5 )}{x ^{2}} : \frac{8 x ^{3} - 5}{x ^{2}}

= \frac{8 x ^{3} - 5}{x ^{2}}

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