derivative (cos(x^3))/2

解

導関数

\frac{cos ( x ^{3} )}{2}

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

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

連鎖法則を適用:

- sin (x^{3}) \frac{d}{d x} (x^{3})

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

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

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

簡素化

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

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