derivative of sqrt(1-cos(x^3))

解

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

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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