derivative of xarcsec(x^3)

解

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

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

解答ステップ

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

積の法則を適用:

(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

簡素化

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}