derivative of arcsin(sqrt(x^2-4))

Lösung

\frac{d}{d x} (arcsin (x^{2} - 4))

\frac{x}{- x ^{2} + 5 x ^{2} - 4}

Schritte zur Lösung

\frac{d}{d x} (arcsin (x^{2} - 4))

Wende die Kettenregel an:

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

= \frac{1}{1 - ( x ^{2} - 4 ) ^{2}} \frac{d}{d x} (x^{2} - 4)

\frac{d}{d x} (x^{2} - 4) = \frac{x}{x ^{2} - 4}

= \frac{1}{1 - ( x ^{2} - 4 ) ^{2}} \cdot \frac{x}{x ^{2} - 4}

Vereinfache

\frac{1}{1 - ( x ^{2} - 4 ) ^{2}} \cdot \frac{x}{x ^{2} - 4} : \frac{x}{- x ^{2} + 5 x ^{2} - 4}

= \frac{x}{- x ^{2} + 5 x ^{2} - 4}

y = e^{- 2 ((x - 146) - 2 (\frac{l n ( 19.52 )}{2}))}

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