derivative of 5x^3-x^{-2/5}

Lösung

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

\frac{2 + 75 x ^{\frac{17}{5}}}{5 x ^{\frac{7}{5}}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (5 x^{3}) = 15 x^{2}

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

= 15 x^{2} - (- \frac{2}{5 x ^{\frac{7}{5}}})

Vereinfache

15 x^{2} - (- \frac{2}{5 x ^{\frac{7}{5}}}) : \frac{2 + 75 x ^{\frac{17}{5}}}{5 x ^{\frac{7}{5}}}

= \frac{2 + 75 x ^{\frac{17}{5}}}{5 x ^{\frac{7}{5}}}

x \to 0 lim (12 + x^{2} ln (x))

\frac{d}{d x} (\frac{5 x ^{2} - 9 x + 7}{3 x + 2})

\int (5 x^{2} + 7 x^{- 2}) d x

\frac{d y}{d x} = \frac{y ^{2}}{1 + x ^{2}}

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