Question

Find the derivative of y with respect to x:
y=(1+cos²x)^6
y'=6(1+cos²x)^5

How do you derive inside the brackets? The answer says -sin2x, but wouldn't it be -2sinx, using the chain rule.

Answer 1

You still have to differentiate the "inside"

d(1+cos^2x) = 2cosx(-sinx)
= -2sinxcox
= -sin 2x, one of the identities

so
y'=6(1+cos²x)^5(-sin2x)
= y'= -6(1+cos²x)^5(sin2x)

Answer 2

Oh, I see it now, thanks!