derivative f(x)=x^{-1/5}+x^{1/5}

Lösung

ableitung von

f (x) = x^{- \frac{1}{5}} + x^{\frac{1}{5}}

- \frac{1}{5 x ^{\frac{6}{5}}} + \frac{1}{5 x ^{\frac{4}{5}}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (x^{\frac{1}{5}}) = \frac{1}{5 x ^{\frac{4}{5}}}

= - \frac{1}{5 x ^{\frac{6}{5}}} + \frac{1}{5 x ^{\frac{4}{5}}}

x \to 1 - lim (G (x))

x \to - \infty lim (- 5^{x})

x \to 0 lim (\frac{x ^{3}}{x ^{2} + x})

x y^{^{'}} + y = - 9 x y^{2}

\int 6 x (x^{2} + 9)^{5} d x