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Beliebt Rechnen >

(\partial)/(\partial x)((3y^2-x^2)/(y^5))

Lösung

\frac{\partial}{\partial x} (\frac{3 y ^{2} - x ^{2}}{y ^{5}})

Lösung

- \frac{2 x}{y ^{5}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{3 y ^{2} - x ^{2}}{y ^{5}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= \frac{1}{y ^{5}} \frac{\partial}{\partial x} (3 y^{2} - x^{2})

Wende die Summen-/Differenzregel an:

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

= \frac{1}{y ^{5}} (\frac{\partial}{\partial x} (3 y^{2}) - \frac{\partial}{\partial x} (x^{2}))

\frac{\partial}{\partial x} (3 y^{2}) = 0

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

= \frac{1}{y ^{5}} (0 - 2 x)

Vereinfache

\frac{1}{y ^{5}} (0 - 2 x) : - \frac{2 x}{y ^{5}}

= - \frac{2 x}{y ^{5}}

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