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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

= 2 \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

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

Vereinfache

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

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

Beliebte Beispiele

derivative of x^{25}

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sum from n=1 to infinity of (1/2)^{99-1}

n = 1 \sum \infty (\frac{1}{2})^{99 - 1}

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d er i v a t i v e f (x) = ln (1 - x)

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\int (\frac{1}{x ^{3}} + 3)^{2} d x

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\int_{2}^{4} \frac{5}{x} d x