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Beliebt Rechnen >

derivative of x^2-3x-5x^{-1}+7x^{-2}

Lösung

\frac{d}{d x} (x^{2} - 3 x - 5 x^{- 1} + 7 x^{- 2})

Lösung

2 x - 3 + \frac{5}{x ^{2}} - \frac{14}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (x^{2} - 3 x - 5 x^{- 1} + 7 x^{- 2})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{2}) - \frac{d}{d x} (3 x) - \frac{d}{d x} (5 x^{- 1}) + \frac{d}{d x} (7 x^{- 2})

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (3 x) = 3

\frac{d}{d x} (5 x^{- 1}) = - \frac{5}{x ^{2}}

\frac{d}{d x} (7 x^{- 2}) = - \frac{14}{x ^{3}}

= 2 x - 3 - (- \frac{5}{x ^{2}}) - \frac{14}{x ^{3}}

Vereinfache

= 2 x - 3 + \frac{5}{x ^{2}} - \frac{14}{x ^{3}}

Graph

Beliebte Beispiele

(dy)/(dx)=(x^2-3)/(6y^2)

\frac{d y}{d x} = \frac{x ^{2} - 3}{6 y ^{2}}

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\frac{d}{d x} (a x + cot (a x))