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Beliebt Rechnen >

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

Lösung

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

Lösung

y^{2} - 3 y x^{2}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

= y^{2} - 3 y x^{2}

Beliebte Beispiele

derivative f(x)=(2x^3+3)^6

d er i v a t i v e f (x) = (2 x^{3} + 3)^{6}

t an g e n t - 2 x^{2}

integral of 9x^2-8x

\int 9 x^{2} - 8 x d x

integral of 3/(sqrt(1+9x^2))

\int \frac{3}{1 + 9 x ^{2}} d x

integral of (sqrt(y^2-4))/y

\int \frac{y ^{2} - 4}{y} d y