(\partial)/(\partial x)(1/(sqrt(x^2)))

Lösung

\frac{\partial}{\partial x} (\frac{1}{x ^{2}})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{x ^{2}})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{1}{x ^{2}}

d er i v a t i v e \frac{x ^{3} - 3}{x ^{2} + 2}

\int_{1}^{5} x d x

\int x^{2} (ln (x))^{2} d x

d er i v a t i v e y = - 6 x

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