(\partial)/(\partial x)(-1/(sqrt(x^2+y^2)))

Lösung

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

\frac{x}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{x}{( x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

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

\int (15 x^{13}) d x

\int 9 x^{2} - 4 x + 3 d x

p \to 4 lim (p^{2} + p + 5)

d er i v a t i v e e^{2 x} cos (5 x)