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Beliebt Rechnen >

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

Lösung

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

Lösung

6 y x + 2 y^{3}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (3 x^{2} y) = 6 y x

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

= 6 y x + 2 y^{3}

Beliebte Beispiele

sum from n=0 to infinity of e^{-1}

n = 0 \sum \infty e^{- 1}

derivative of ln(x^2+3x)

\frac{d}{d x} (ln (x^{2} + 3 x))

derivative of 5(1-e^{-2x})

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

derivative of sqrt(x^2+y^2-4)

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

limit as x approaches-1 of (x^2+1)/(x+1)

x \to - 1 lim (\frac{x ^{2} + 1}{x + 1})