derivative of 5/(2x^2)

Lösung

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

- \frac{5}{x ^{3}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

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

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

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Vereinfache

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

= - \frac{5}{x ^{3}}

a re a x = y^{2} - 4 y, x = 2 y - y^{2}

\int \frac{1}{t ^{2} 400 - t ^{2}} d t

\frac{d}{d x} (cos (arctan (3 x)))

\int_{0}^{\frac{1}{10}} x ln (10 x) d x

x \to 0 lim (2)