derivative of 2x^6-5x^{-1/2}

Lösung

\frac{d}{d x} (2 x^{6} - 5 x^{- \frac{1}{2}})

\frac{5 + 24 x ^{\frac{13}{2}}}{2 x ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (2 x^{6} - 5 x^{- \frac{1}{2}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (2 x^{6}) - \frac{d}{d x} (5 x^{- \frac{1}{2}})

\frac{d}{d x} (2 x^{6}) = 12 x^{5}

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

= 12 x^{5} - (- \frac{5}{2 x ^{\frac{3}{2}}})

Vereinfache

12 x^{5} - (- \frac{5}{2 x ^{\frac{3}{2}}}) : \frac{5 + 24 x ^{\frac{13}{2}}}{2 x ^{\frac{3}{2}}}

= \frac{5 + 24 x ^{\frac{13}{2}}}{2 x ^{\frac{3}{2}}}

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