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Beliebt Rechnen >

derivative of arcsin(x-sqrt(1-x^2))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

y^'=(-y)/(40-t)

y^{^{'}} = \frac{- y}{40 - t}

integral of 2(1+tan^2(a))

\int 2 (1 + tan^{2} (a)) d a

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x \to 0 lim (sec^{2} (x))

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\int (4 x - 8 y^{3}) d y

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\int - \frac{1}{4} cos (2 x) d x