(\partial)/(\partial x)(arccos(y/x))

Lösung

\frac{\partial}{\partial x} (arccos (\frac{y}{x}))

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

Schritte zur Lösung

\frac{\partial}{\partial x} (arccos (\frac{y}{x}))

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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