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Beliebt Rechnen >

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

Lösung

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

Lösung

3 y^{2} - 4 x y + x^{2}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (x - y)^{2}, g = y

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

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

\frac{\partial}{\partial y} (y) = 1

= (- 2 (x - y)) y + 1 \cdot (x - y)^{2}

Vereinfache

(- 2 (x - y)) y + 1 \cdot (x - y)^{2} : 3 y^{2} - 4 x y + x^{2}

= 3 y^{2} - 4 x y + x^{2}

Beliebte Beispiele

(\partial)/(\partial x)(3arctan(x/y))

\frac{\partial}{\partial x} (3 arctan (\frac{x}{y}))

y^{''}-8y^'+15y=-sin(2t)

y^{^{''}} - 8 y^{^{'}} + 15 y = - sin (2 t)

y^{''}-2y^'+26y=e^xsin(x)

y^{^{''}} - 2 y^{^{'}} + 26 y = e^{x} sin (x)

(\partial)/(\partial x)(e^{2x+8y})

\frac{\partial}{\partial x} (e^{2 x + 8 y})

tangent 8sqrt(x)

t an g e n t 8 x