derivative 1/(\sqrt[5]{x^2)}

Lösung

ableitung von

\frac{1}{5 x ^{2}}

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

Schritte zur Lösung

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

4 y^{^{''}} + 5 y = 0

\frac{d}{d x} (ln (x - 2 y))

d er i v a t i v e f (x) = x 4 - x^{2}

t a y l or f (x) = e^{2 x}

n = 0 \sum \infty (\frac{1}{3})^{n + 1}