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Beliebt Rechnen >

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

Lösung

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

Lösung

4 y - 4 x^{3}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

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

Vereinfache

= 4 y - 4 x^{3}

Beliebte Beispiele

integral from 0 to x of e^{-t^2}

\int_{0}^{x} e^{- t^{2}} d t

derivative (x+1)/(4x^2+12x+2)

d er i v a t i v e \frac{x + 1}{4 x ^{2} + 12 x + 2}

derivative of 3arcsin(x^2)

\frac{d}{d x} (3 arcsin (x^{2}))

integral from 1 to 2 of 4^x

\int_{1}^{2} 4^{x} d x

fläche 4x^2,(sqrt(x))/2

a re a 4 x^{2}, \frac{x}{2}