(\partial)/(\partial x)(a/(x^2))

Lösung

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

- \frac{2 a}{x ^{3}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Potenzregel an:

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

= a (- 2 x^{- 2 - 1})

Vereinfache

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

= - \frac{2 a}{x ^{3}}

\frac{\partial}{\partial x} (ln (x^{6} y))

\frac{d y}{d x} + \frac{y}{x} = 8 x^{5} y^{2}

\int_{0}^{6} \frac{8 t}{( t - 7 ) ^{2}} d t

\frac{\partial}{\partial x} (\frac{z ( x + y )}{x + y + z})

x^{^{'}} = - 2 x