Find dy/dx for y = cos^4(2x)Step by step process

We have to find the derivative of y = (cos 2x)^4. We need to use the chain rule here:

y' = [(cos 2x)^4]'

=> 4*(cos 2x)^(4 - 1)*(cos 2x)'

=> 4*(cos 2x)^3*(-sin 2x)*(2x)'

=> 4*(cos 2x)^3*(-sin 2x)*2

=> -8*(cos 2x)^3*(sin 2x)

The required derivative is -8*(cos 2x)^3*(sin 2x)

Unlock This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

We have to find the derivative of y = (cos 2x)^4. We need to use the chain rule here:

y' = [(cos 2x)^4]'

=> 4*(cos 2x)^(4 - 1)*(cos 2x)'

=> 4*(cos 2x)^3*(-sin 2x)*(2x)'

=> 4*(cos 2x)^3*(-sin 2x)*2

=> -8*(cos 2x)^3*(sin 2x)

The required derivative is -8*(cos 2x)^3*(sin 2x)

Approved by eNotes Editorial Team

Given y= cos^4 (2x)

We need to find dy/dx

We will use the chain rule to find the derivative.

Let u= cos2x ==> u' = -2sin(2x)

==> y= u^4

==> y' = 4u^3 * u'

Now we will substitute with u= cos2x

==> y' = 4(cos^3 2x) * -2sin2x

==> dy/dx = -8sin2x*cos^2 2x

Approved by eNotes Editorial Team