derivative of (7x^2-1/x)

Lösung

\frac{d}{d x} (\frac{7 x ^{2} - 1}{x})

\frac{7 x ^{2} + 1}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7 x ^{2} - 1}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 7 x ^{2} - 1 ) x - \frac{d x}{d x} ( 7 x ^{2} - 1 )}{x ^{2}}

\frac{d}{d x} (7 x^{2} - 1) = 14 x

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

= \frac{14 xx - 1 \cdot ( 7 x ^{2} - 1 )}{x ^{2}}

Vereinfache

\frac{14 xx - 1 \cdot ( 7 x ^{2} - 1 )}{x ^{2}} : \frac{7 x ^{2} + 1}{x ^{2}}

= \frac{7 x ^{2} + 1}{x ^{2}}

y^{^{''}} + 4 y = 0, y (0) = 1, y^{^{'}} (0) = 4

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\int [\frac{a ^{3}}{x ^{2} + a ^{2}}]^{2} d x

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\int cos (4 x - 3) d x