derivative of cos(arctan(5x))

解

\frac{d}{d x} (cos (arctan (5 x)))

- \frac{25 x}{( 25 x ^{2} + 1 ) 1 + 25 x ^{2}}

解答ステップ

\frac{d}{d x} (cos (arctan (5 x)))

連鎖法則を適用:

- sin (arctan (5 x)) \frac{d}{d x} (arctan (5 x))

= - sin (arctan (5 x)) \frac{d}{d x} (arctan (5 x))

\frac{d}{d x} (arctan (5 x)) = \frac{5}{25 x ^{2} + 1}

= - sin (arctan (5 x)) \frac{5}{25 x ^{2} + 1}

簡素化

- sin (arctan (5 x)) \frac{5}{25 x ^{2} + 1} : - \frac{25 x}{( 25 x ^{2} + 1 ) 1 + 25 x ^{2}}

= - \frac{25 x}{( 25 x ^{2} + 1 ) 1 + 25 x ^{2}}