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Beliebt Rechnen >

(\partial)/(\partial x)(x^3-3xy^2)

Lösung

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

Lösung

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

Schritte zur Lösung

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

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

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

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

Beliebte Beispiele

derivative of 2/(1-x^2)

\frac{d}{d x} (\frac{2}{1 - x ^{2}})

integral of 1/(2x-1)

\int \frac{1}{2 x - 1} d x

derivative of (5sqrt(1-x^3)/6)

\frac{d}{d x} (\frac{5 1 - x ^{3}}{6})

integral of 13arctan(sqrt(x))

\int 13 arctan (x) d x

limit as x approaches+0 of (e^{2x}-1)/(sin(3x))

x \to + 0 lim (\frac{e ^{2 x} - 1}{sin ( 3 x )})