derivative of (cos(pix-16)^4)

解

\frac{d}{d x} ((cos (π x - 16))^{4})

- 4 π cos^{3} (π x - 16) sin (π x - 16)

解答ステップ

\frac{d}{d x} ((cos (π x - 16))^{4})

連鎖法則を適用:

4 (cos (π x - 16))^{3} \frac{d}{d x} (cos (π x - 16))

= 4 (cos (π x - 16))^{3} \frac{d}{d x} (cos (π x - 16))

\frac{d}{d x} (cos (π x - 16)) = - sin (π x - 16) π

= 4 (cos (π x - 16))^{3} (- sin (π x - 16) π)

簡素化

= - 4 π cos^{3} (π x - 16) sin (π x - 16)