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Beliebt Rechnen >

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

Lösung

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

Lösung

3 x^{2} - 2 x y - y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

= 3 x^{2} + 0 - 2 y x - y

Vereinfache

= 3 x^{2} - 2 x y - y

Beliebte Beispiele

d/(dt)(5e^tcos(t))

\frac{d}{d t} (5 e^{t} cos (t))

derivative f(x)=cos(5x)

d er i v a t i v e f (x) = cos (5 x)

12x^3-3ysqrt(x^4+1)y^'=0

12 x^{3} - 3 y x^{4} + 1 y^{^{'}} = 0

integral of (e^u)/u

\int \frac{e ^{u}}{u} d u

derivative (x^2+4)^3

d er i v a t i v e (x^{2} + 4)^{3}