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Beliebt Rechnen >

(\partial)/(\partial x)(x^2y+yln(xz^3))

Lösung

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

Lösung

2 y x + \frac{y}{x}

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

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

= 2 y x + \frac{y}{x}

Beliebte Beispiele

integral of 3x^4+7/4 x^5

\int 3 x^{4} + \frac{7}{4} x^{5} d x

derivative y=2ln(3)+1/2 ln(x^2+1)

d er i v a t i v e y = 2 ln (3) + \frac{1}{2} ln (x^{2} + 1)

derivative of 2x(4-x^2^{1/2})

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

integral of sex^2x

\int se x^{2} x d x

\int k y d y