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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

Vereinfache

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

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

\frac{d}{d x} (lo g_{10} (x^{2} + y))

\frac{\partial}{\partial x} (- 2 e^{- x^{2} - y^{2}} x cos (x y) - e^{- x^{2} - y^{2}} y sin (x y))

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

\frac{\partial}{\partial x} (5 x y^{4} + 2 y cos (x))

d er i v a t i v e y = x^{3} e^{4 x}