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Beliebt Rechnen >

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

Lösung

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

Lösung

6 x y

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial y} (x^{3}) = 0

\frac{\partial}{\partial y} (3 x) = 0

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

= 0 - 0 + 6 x y

Vereinfache

= 6 x y

Beliebte Beispiele

derivative f(x)=7-x^2

d er i v a t i v e f (x) = 7 - x^{2}

3 x^{2} y d x + y d y = 0

limit as x approaches 1 of x+1/x

x \to 1 lim (x + \frac{1}{x})

tangent y= 1/(x^3),(-3,-1/27)

t an g e n t y = \frac{1}{x ^{3}}, (- 3, - \frac{1}{27})

derivative of 6x-7

\frac{d}{d x} (6 x - 7)