derivative of xarcsec(x^3)

Lösung

\frac{d}{d x} (x arcsec (x^{3}))

arcsec (x^{3}) + \frac{3}{x ^{6} - 1}

Schritte zur Lösung

\frac{d}{d x} (x arcsec (x^{3}))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = arcsec (x^{3})

= \frac{d x}{d x} arcsec (x^{3}) + \frac{d}{d x} (arcsec (x^{3})) x

\frac{d x}{d x} = 1

\frac{d}{d x} (arcsec (x^{3})) = \frac{3}{x x ^{6} - 1}

= 1 \cdot arcsec (x^{3}) + \frac{3}{x x ^{6} - 1} x

Vereinfache

1 \cdot arcsec (x^{3}) + \frac{3}{x x ^{6} - 1} x : arcsec (x^{3}) + \frac{3}{x ^{6} - 1}

= arcsec (x^{3}) + \frac{3}{x ^{6} - 1}

in v erse l a pl a ce \frac{( 6 + 6 s )}{2 s ^{2} + 1}

d er i v a t i v e 9 x^{\frac{1}{2}}

x \to 0 lim (\frac{( sin ( 3 x ) )}{x})

x^{2} y^{^{''}} - 5 x y^{^{'}} + 9 y = 0

x \to 2 lim (x^{2} - 7 x + 5)