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

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epic2121 | Student | (Level 1) Honors

Posted June 2, 2011 at 12:04 PM via web

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

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted June 2, 2011 at 12:15 PM (Answer #1)

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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

 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 2, 2011 at 12:26 PM (Answer #2)

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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)

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