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Beliebt Rechnen >

(\partial)/(\partial x)(e^{-xy}+y^3x^4)

Lösung

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

Lösung

- y e^{- y x} + 4 y^{3} x^{3}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (e^{- x y}) + \frac{\partial}{\partial x} (y^{3} x^{4})

\frac{\partial}{\partial x} (e^{- x y}) = - y e^{- y x}

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

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

Beliebte Beispiele

derivative of 3x^3+2x^2-1x+5

\frac{d}{d x} (3 x^{3} + 2 x^{2} - 1 x + 5)

integral from 0 to 3 of e^{-x^2}

\int_{0}^{3} e^{- x^{2}} d x

limit as x approaches pi of ln(cos(x)-3)

x \to π lim (ln (cos (x) - 3))

integral of y^2z+2xz^2

\int y^{2} z + 2 x z^{2} d x

d er i v a t i v e \frac{2}{x}