Question

Y=cot^3*3πx/2

Answer 1

Chắc đề là tính đạo hàm của \(y=cot^3\left(\dfrac{3\pi x}{2}\right)\)?

Nếu vậy:

\(y'=3cot^2\left(\dfrac{3\pi x}{2}\right).\left[cot\left(\dfrac{3\pi x}{2}\right)\right]'=3cot^2\left(\dfrac{3\pi x}{2}\right).\left(-\dfrac{1}{sin^2\left(\dfrac{3\pi x}{2}\right)}\right).\dfrac{3\pi}{2}\)

\(=-\dfrac{9\pi}{2}.\dfrac{cos^2\left(\dfrac{3\pi x}{2}\right)}{sin^4\left(\dfrac{3\pi x}{2}\right)}\)