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Beliebt Rechnen >

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

Lösung

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

Lösung

2 y^{3} x + 8 y x^{3}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial x} (2 x^{4} y) = 8 y x^{3}

= 2 y^{3} x + 8 y x^{3}

Beliebte Beispiele

derivative of 3x^4-5x^2+1

\frac{d}{d x} (3 x^{4} - 5 x^{2} + 1)

d/(dy)((2x)/(x^2+y^2))

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

derivative of (4-x^2^3)

\frac{d}{d x} ((4 - x^{2})^{3})

integral of (sin(2/x))/(x^2)

\int \frac{sin ( \frac{2}{x} )}{x ^{2}} d x

derivative of 5/3 x^2y^{-2}

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