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Beliebt Rechnen >

(\partial)/(\partial x)((a-b^2)/(x-c^2))

Lösung

\frac{\partial}{\partial x} (\frac{a - b ^{2}}{x - c ^{2}})

Lösung

- \frac{a - b ^{2}}{( x - c ^{2} ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{a - b ^{2}}{x - c ^{2}})

Behandle

a, b, c

als Konstanten

Entferne die Konstante:

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

= (a - b^{2}) \frac{\partial}{\partial x} (\frac{1}{x - c ^{2}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= (a - b^{2}) \frac{\partial}{\partial x} ((x - c^{2})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( x - c ^{2} ) ^{2}} \frac{\partial}{\partial x} (x - c^{2})

= - \frac{1}{( x - c ^{2} ) ^{2}} \frac{\partial}{\partial x} (x - c^{2})

\frac{\partial}{\partial x} (x - c^{2}) = 1

= (a - b^{2}) (- \frac{1}{( x - c ^{2} ) ^{2}} \cdot 1)

Vereinfache

(a - b^{2}) (- \frac{1}{( x - c ^{2} ) ^{2}} \cdot 1) : - \frac{a - b ^{2}}{( x - c ^{2} ) ^{2}}

= - \frac{a - b ^{2}}{( x - c ^{2} ) ^{2}}

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