d/(d{x)}(({x}^2+{y}^2+{z}^2)^{(-1)/2})

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \to 0 + lim (x ln (x^{5}))

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

s l o p e x^{2} + y^{2} = 27, at x = 3

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

d er i v a t i v e (x + 1)^{81}