derivative (3x^3+7)/x

Lösung

ableitung von

\frac{3 x ^{3} + 7}{x}

\frac{6 x ^{3} - 7}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x ^{3} + 7}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x ^{3} + 7 ) x - \frac{d x}{d x} ( 3 x ^{3} + 7 )}{x ^{2}}

\frac{d}{d x} (3 x^{3} + 7) = 9 x^{2}

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

= \frac{9 x ^{2} x - 1 \cdot ( 3 x ^{3} + 7 )}{x ^{2}}

Vereinfache

\frac{9 x ^{2} x - 1 \cdot ( 3 x ^{3} + 7 )}{x ^{2}} : \frac{6 x ^{3} - 7}{x ^{2}}

= \frac{6 x ^{3} - 7}{x ^{2}}

\frac{d}{d x} ((3 x - 1)^{4})

\frac{d}{d x} (- cos (2 x) - sin (2 x) - \frac{1}{5} e^{x})

2 \frac{d y}{d x} + 6 y = 3

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\int \frac{x ^{2}}{x ^{3} + 2} d x