derivative f(x)=cos(arctan(x))

解

導関数

f (x) = cos (arctan (x))

- \frac{x}{( x ^{2} + 1 ) 1 + x ^{2}}

解答ステップ

\frac{d}{d x} (cos (arctan (x)))

連鎖法則を適用:

- sin (arctan (x)) \frac{d}{d x} (arctan (x))

= - sin (arctan (x)) \frac{d}{d x} (arctan (x))

\frac{d}{d x} (arctan (x)) = \frac{1}{x ^{2} + 1}

= - sin (arctan (x)) \frac{1}{x ^{2} + 1}

簡素化

- sin (arctan (x)) \frac{1}{x ^{2} + 1} : - \frac{x}{( x ^{2} + 1 ) 1 + x ^{2}}

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