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Beliebt Rechnen >

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

Lösung

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

Lösung

3 x^{2} - 6 x

Schritte zur Lösung

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

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

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

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

\frac{\partial}{\partial x} (3 x^{2}) = 6 x

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

= 3 x^{2} + 0 - 6 x + 0

Vereinfache

= 3 x^{2} - 6 x

Beliebte Beispiele

d/(da)(1+cos^4(a)-sin^4(a))

\frac{d}{d a} (1 + cos^{4} (a) - sin^{4} (a))

limit as x approaches infinity of (2x)/x

x \to \infty lim (\frac{2 x}{x})

implicit (dy)/(dx),y=x^3+2

im pl i c i t \frac{d y}{d x}, y = x^{3} + 2

limit as x approaches infinity of e^0

x \to \infty lim (e^{0})

derivative of 9x^2+6x-2

\frac{d}{d x} (9 x^{2} + 6 x - 2)