how to differentiate cos^6(x)?

Rewrite the expression as:

y = [cos(x)]^6

Now take the derivative by applying the chain rule:

dy/dx = 6[cos(x)]^5 * -sin(x)

dy/dx = -6sin(x)cos^5(x)

remember

derivative of x^n = nx^(n-1)

derivative of composite functions [f(x)]^n = n[f(x)]^(n-1) * f '(x) (chain rule)

derivative of cos is - sin

may be simpler to write your function as

(cos x)^6

derivative is

6(cos x)^5 (-sin x)

-6 (sin x)(cos x)^5

hope it helps

(remember that choosing best answer makes you earn 3 points :)

It is y = (cosx)^6 ... we must use chain rule... find the derivative of cosx, the derivative of the power 6 and multiply.

It is y ´= (-sinx)* 6(cosx)^5 OK!