How do I take the derivative of (cos(x))^3? Arethese right? -- 3(-sin(x))^2 *cos(x)=-3cos(x)(sin(x))^2

Question

How do I take the derivative of (cos(x))^3? Arethese right? --> 3(-sin(x))^2 *cos(x)=-3cos(x)(sin(x))^2

Reiny · Accepted Answer

not quite, by the chain rule y = (cos x)^3 dy/dx = 3(cosx)^2 (-sinx)

oobleck · Answer

Just expanding on Reiny's answer, consider u = cos^3 x Then y = u^3 so y' = 3u^2 u' = 3cos^2x (-sinx) You squared the derivative - tsk tsk