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Beliebt Rechnen >

(\partial)/(\partial y)(4/3 pi(x^3-y^3))

Lösung

\frac{\partial}{\partial y} (\frac{4}{3} π (x^{3} - y^{3}))

Lösung

- 4 π y^{2}

Schritte zur Lösung

\frac{\partial}{\partial y} (\frac{4}{3} π (x^{3} - y^{3}))

Vereinfache

\frac{4}{3} π (x^{3} - y^{3}) : \frac{4 π}{3} (x^{3} - y^{3})

= \frac{\partial}{\partial y} (\frac{4 π}{3} (x^{3} - y^{3}))

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{4 π}{3} \frac{\partial}{\partial y} (x^{3} - y^{3})

Wende die Summen-/Differenzregel an:

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

= \frac{4 π}{3} (\frac{\partial}{\partial y} (x^{3}) - \frac{\partial}{\partial y} (y^{3}))

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

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

= \frac{4 π}{3} (0 - 3 y^{2})

Vereinfache

\frac{4 π}{3} (0 - 3 y^{2}) : - 4 π y^{2}

= - 4 π y^{2}

Beliebte Beispiele

limit as x approaches infinity of 3/(5x)

x \to \infty lim (\frac{3}{5 x})

integral of 9e^{3x}

\int 9 e^{3 x} d x

integral of xe^{3x}+e^x

\int x e^{3 x} + e^{x} d x

derivative f(x)=e^{2x}(x^3+1)

d er i v a t i v e f (x) = e^{2 x} (x^{3} + 1)

(d^2)/(dx^2)((4x^2+9x)cos(x))

\frac{d ^{2}}{d x ^{2}} ((4 x^{2} + 9 x) cos (x))