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

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e \frac{x ^{2}}{3 ( 1 - x )}

d er i v a t i v e (4 x - 3)^{4}

\int x arctan (7 x) d x

z \to 0 lim (\frac{sin ( z )}{z})

d er i v a t i v e f (x) = \frac{4}{x ^{5}}