derivative of sqrt(x)-3x^2+8x^{-2}

Lösung

\frac{d}{d x} (x - 3 x^{2} + 8 x^{- 2})

\frac{x ^{\frac{5}{2}} - 32 - 12 x ^{4}}{2 x ^{\frac{5}{2}} x}

Schritte zur Lösung

\frac{d}{d x} (x - 3 x^{2} + 8 x^{- 2})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x) - \frac{d}{d x} (3 x^{2}) + \frac{d}{d x} (8 x^{- 2})

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (3 x^{2}) = 6 x

\frac{d}{d x} (8 x^{- 2}) = - \frac{16}{x ^{3}}

= \frac{1}{2 x} - 6 x - \frac{16}{x ^{3}}

Vereinfache

\frac{1}{2 x} - 6 x - \frac{16}{x ^{3}} : \frac{x ^{\frac{5}{2}} - 32 - 12 x ^{4}}{2 x ^{\frac{5}{2}} x}

= \frac{x ^{\frac{5}{2}} - 32 - 12 x ^{4}}{2 x ^{\frac{5}{2}} x}

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