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Beliebt Rechnen >

(\partial)/(\partial x)(x^2-y^2+5xy)

Lösung

\frac{\partial}{\partial x} (x^{2} - y^{2} + 5 x y)

Lösung

2 x + 5 y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} - y^{2} + 5 x y)

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} (y^{2}) + \frac{\partial}{\partial x} (5 x y)

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

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

\frac{\partial}{\partial x} (5 x y) = 5 y

= 2 x - 0 + 5 y

Vereinfache

= 2 x + 5 y

Beliebte Beispiele

sum from m=1 to infinity of 3*(1/3)

m = 1 \sum \infty 3 \cdot (\frac{1}{3})

integral of (x-3)^2sin(x-3)

\int (x - 3)^{2} sin (x - 3) d x

integral of 8tan(8x)

\int 8 tan (8 x) d x

limit as x approaches 9 of sqrt(25-x)

x \to 9 lim (25 - x)

tangent f(x)=3x^2-10x

t an g e n t f (x) = 3 x^{2} - 10 x