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Beliebt Rechnen >

(\partial)/(\partial x)((x^3+5)/(y^3-1))

Lösung

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

Lösung

\frac{3 x ^{2}}{y ^{3} - 1}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial x} (5) = 0

= \frac{1}{y ^{3} - 1} (3 x^{2} + 0)

Vereinfache

\frac{1}{y ^{3} - 1} (3 x^{2} + 0) : \frac{3 x ^{2}}{y ^{3} - 1}

= \frac{3 x ^{2}}{y ^{3} - 1}

Beliebte Beispiele

derivative of arccos(e^{3x})

\frac{d}{d x} (arccos (e^{3 x}))

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\int (x^{4} + 5)^{3} x^{3} d x

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\frac{d}{d x} (cos^{2} (x) sin^{2} (x))