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Beliebt Rechnen >

(\partial)/(\partial x)(sqrt(x^2+y^2+z^2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial 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}}

Beliebte Beispiele

integral of 2/((1-x)^2)

\int \frac{2}{( 1 - x ) ^{2}} d x

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\int 14 x^{15} e^{x^{8}} d x

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\int (x - 2) sin (π x) d x