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Beliebt Rechnen >

(\partial)/(\partial x)(-x^3+4xy-2y^2+1)

Lösung

\frac{\partial}{\partial x} (- x^{3} + 4 x y - 2 y^{2} + 1)

Lösung

4 y - 3 x^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (- x^{3} + 4 x y - 2 y^{2} + 1)

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} (4 x y) - \frac{\partial}{\partial x} (2 y^{2}) + \frac{\partial}{\partial x} (1)

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

\frac{\partial}{\partial x} (4 x y) = 4 y

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

\frac{\partial}{\partial x} (1) = 0

= - 3 x^{2} + 4 y - 0 + 0

Vereinfache

= 4 y - 3 x^{2}

Beliebte Beispiele

limit as x approaches 7 of 2x+5

x \to 7 lim (2 x + 5)

derivative of (x+4^2)

\frac{d}{d x} ((x + 4)^{2})

integral of (5x-1)^7

\int (5 x - 1)^{7} d x

fläche 2x,9x-x^2,(7,14)

a re a 2 x, 9 x - x^{2}, (7, 14)

derivative f(x)= 6/(ln(x^2+4))

d er i v a t i v e f (x) = \frac{6}{ln ( x ^{2} + 4 )}