derivative of arcsec(x^3)

解

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

\frac{3}{x x ^{6} - 1}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

\frac{1}{( x ^{3} ) ^{2} ( x ^{3} ) ^{2} - 1} \cdot 3 x^{2} : \frac{3}{x x ^{6} - 1}

= \frac{3}{x x ^{6} - 1}