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Beliebt Rechnen >

derivative of (2x^2-3x+1/x)

Lösung

\frac{d}{d x} (\frac{2 x ^{2} - 3 x + 1}{x})

Lösung

\frac{2 x ^{2} - 1}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{2} - 3 x + 1}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x ^{2} - 3 x + 1 ) x - \frac{d x}{d x} ( 2 x ^{2} - 3 x + 1 )}{x ^{2}}

\frac{d}{d x} (2 x^{2} - 3 x + 1) = 4 x - 3

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

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

Vereinfache

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

= \frac{2 x ^{2} - 1}{x ^{2}}

Graph

Beliebte Beispiele

steigung x^2+xy+2y^2=28,(2,3)

s l o p e x^{2} + x y + 2 y^{2} = 28, (2, 3)

t^2y^{''}+7ty^'+10y=0

t^{2} y^{^{''}} + 7 t y^{^{'}} + 10 y = 0

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\int tan (4 x) sec^{5} (4 x) d x

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x \to 7 - lim (\frac{1}{x - 7})

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d er i v a t i v e x^{2} + 6