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Beliebt Rechnen >

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

Lösung

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

Lösung

2 x - 2 y

Schritte zur Lösung

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

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

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

\frac{\partial}{\partial x} (4 y^{2}) = 0

= 2 x - 2 y + 0

Vereinfache

= 2 x - 2 y

Beliebte Beispiele

limit as x approaches 6 of 6*5/6*(-2/3)

x \to 6 lim (6 \cdot \frac{5}{6} \cdot (- \frac{2}{3}))

derivative g(x)=x^2(1-9x)

d er i v a t i v e g (x) = x^{2} (1 - 9 x)

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

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

(\partial)/(\partial y)(ycos(xy))

\frac{\partial}{\partial y} (y cos (x y))

integral of (e^x)/(5-e^{2x)}

\int \frac{e ^{x}}{5 - e ^{2 x}} d x