derivative cos(sqrt(sin(cot(pix))))

解

導関数

cos (sin (cot (π x)))

- sin (sin (cot (π x))) \frac{1}{2 sin ( cot ( π x ) )} cos (cot (π x)) (- csc^{2} (π x) π)

解答ステップ

\frac{d}{d x} (cos (sin (cot (π x))))

連鎖法則を適用:

- sin (sin (cot (π x))) \frac{d}{d x} (sin (cot (π x)))

= - sin (sin (cot (π x))) \frac{d}{d x} (sin (cot (π x)))

\frac{d}{d x} (sin (cot (π x))) = \frac{1}{2 sin ( cot ( π x ) )} cos (cot (π x)) (- csc^{2} (π x) π)

= - sin (sin (cot (π x))) \frac{1}{2 sin ( cot ( π x ) )} cos (cot (π x)) (- csc^{2} (π x) π)