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Beliebt Rechnen >

(\partial)/(\partial x)(12x^4-6x^2y+4y^3)

Lösung

\frac{\partial}{\partial x} (12 x^{4} - 6 x^{2} y + 4 y^{3})

Lösung

48 x^{3} - 12 x y

Schritte zur Lösung

\frac{\partial}{\partial x} (12 x^{4} - 6 x^{2} y + 4 y^{3})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (12 x^{4}) - \frac{\partial}{\partial x} (6 x^{2} y) + \frac{\partial}{\partial x} (4 y^{3})

\frac{\partial}{\partial x} (12 x^{4}) = 48 x^{3}

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

\frac{\partial}{\partial x} (4 y^{3}) = 0

= 48 x^{3} - 12 y x + 0

Vereinfache

= 48 x^{3} - 12 x y

Beliebte Beispiele

derivative of x^{3/5}(4-x)

\frac{d}{d x} (x^{\frac{3}{5}} (4 - x))

derivative arccos(e^{2x})

d er i v a t i v e arccos (e^{2 x})

integral from 0 to 2 of 1/(x^{1.9)}

\int_{0}^{2} \frac{1}{x ^{1.9}} d x

derivative f(x)=(x+3)/(x+5)

d er i v a t i v e f (x) = \frac{x + 3}{x + 5}

(\partial)/(\partial u)(3u^2)

\frac{\partial}{\partial u} (3 u^{2})