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Beliebt Rechnen >

(\partial)/(\partial x)(x^4-4x^3y+6x^2y^2)

Lösung

\frac{\partial}{\partial x} (x^{4} - 4 x^{3} y + 6 x^{2} y^{2})

Lösung

4 x^{3} - 12 y x^{2} + 12 y^{2} x

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{4} - 4 x^{3} y + 6 x^{2} y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{4}) - \frac{\partial}{\partial x} (4 x^{3} y) + \frac{\partial}{\partial x} (6 x^{2} y^{2})

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

\frac{\partial}{\partial x} (4 x^{3} y) = 12 y x^{2}

\frac{\partial}{\partial x} (6 x^{2} y^{2}) = 12 y^{2} x

= 4 x^{3} - 12 y x^{2} + 12 y^{2} x

Beliebte Beispiele

steigung-3x^2-2xy+3y^3=57,(-4,3)

s l o p e - 3 x^{2} - 2 x y + 3 y^{3} = 57, (- 4, 3)

integral of 1/(1-sin(1/2 x))

\int \frac{1}{1 - sin ( \frac{1}{2} x )} d x

t^2y^{''}+ty^'+4y=0

t^{2} y^{^{''}} + t y^{^{'}} + 4 y = 0

integral of 3x^3cos(5x)

\int 3 x^{3} cos (5 x) d x

limit as x approaches 5 of sqrt(x^2+11)

x \to 5 lim (x^{2} + 11)