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

Lösung

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

\frac{x}{x ^{2} + y ^{2} + z ^{2}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

= \frac{1}{2 x ^{2} + y ^{2} + z ^{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}} \cdot 2 x

Vereinfache

\frac{1}{2 x ^{2} + y ^{2} + z ^{2}} \cdot 2 x : \frac{x}{x ^{2} + y ^{2} + z ^{2}}

= \frac{x}{x ^{2} + y ^{2} + z ^{2}}

d er i v a t i v e \frac{5}{4 ( x ^{3} + 2 ) ^{3}}

x \to 4 lim (16)

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

x \to \infty lim (x^{7})

\int cos (30) d x