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Beliebt Rechnen >

derivative arccos(sqrt(1-x^2))

Lösung

ableitung von

arccos (1 - x^{2})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (arccos (1 - x^{2}))

Wende die Kettenregel an:

- \frac{1}{1 - ( 1 - x ^{2} ) ^{2}} \frac{d}{d x} (1 - x^{2})

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

tangent y=2x^2+5x

t an g e n t y = 2 x^{2} + 5 x

integral of (sqrt(x)+1/(9sqrt(x)))

\int (x + \frac{1}{9 x}) d x

integral of ln(1+x^3)

\int ln (1 + x^{3}) d x

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(\partial}{\partial y}(\frac{3x)/y)

\frac{\partial}{\partial y} (\frac{3 x}{y})