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Beliebt Rechnen >

(\partial)/(\partial x)(x^2-4xy+3y^2)

Lösung

\frac{\partial}{\partial x} (x^{2} - 4 x y + 3 y^{2})

Lösung

2 x - 4 y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} - 4 x y + 3 y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{2}) - \frac{\partial}{\partial x} (4 x y) + \frac{\partial}{\partial x} (3 y^{2})

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

\frac{\partial}{\partial x} (4 x y) = 4 y

\frac{\partial}{\partial x} (3 y^{2}) = 0

= 2 x - 4 y + 0

Vereinfache

= 2 x - 4 y

Beliebte Beispiele

integral from 0 to 2pi of e^{ix}

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integral of e^{x^7}

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limit as x approaches 0 of ((5^x-1))/x

x \to 0 lim (\frac{( 5 ^{x} - 1 )}{x})

2 y^{^{'}} = y