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Beliebt Rechnen >

derivative arcsin(2/(x^2))

Lösung

ableitung von

arcsin (\frac{2}{x ^{2}})

Lösung

- \frac{4 x ^{4}}{x ^{3} x ^{4} - 4}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{2}{x ^{2}}) = - \frac{4}{x ^{3}}

= \frac{1}{1 - ( \frac{2}{x ^{2}} ) ^{2}} (- \frac{4}{x ^{3}})

Vereinfache

\frac{1}{1 - ( \frac{2}{x ^{2}} ) ^{2}} (- \frac{4}{x ^{3}}) : - \frac{4 x ^{4}}{x ^{3} x ^{4} - 4}

= - \frac{4 x ^{4}}{x ^{3} x ^{4} - 4}

Graph

Beliebte Beispiele

integral from 4 to 9 of 2xsqrt(x)

\int_{4}^{9} 2 x x d x

sin(x)dy=ycos(x)dx

sin (x) d y = y cos (x) d x

y^{''}-2y^'+10y=0,y(0)=-2,y^'(0)=5

y^{^{''}} - 2 y^{^{'}} + 10 y = 0, y (0) = - 2, y^{^{'}} (0) = 5

derivative of (8-3x^2^3)

\frac{d}{d x} ((8 - 3 x^{2})^{3})

y^'=xln(x),y(1)=2

y^{^{'}} = x ln (x), y (1) = 2