(\partial)/(\partial x)((x^3-y^2)^{(-1)})

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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