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Beliebt Rechnen >

(\partial)/(\partial x)(ysqrt(x^2+y^2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Beliebte Beispiele

limit as x approaches infinity of 3x^3-1000x^2

x \to \infty lim (3 x^{3} - 1000 x^{2})

integral of 1/(x^2-2x-3)

\int \frac{1}{x ^{2} - 2 x - 3} d x

integral of sqrt(121-t^2)

\int 121 - t^{2} d t

derivative of 7xy

\frac{d}{d x} (7 x y)

derivative of arcsec(2x+1)

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