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Find dy/dx for y = cos^4(2x)Step by step process
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High School Teacher
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
Posted by hala718 on June 2, 2011 at 12:15 PM (Answer #1)
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)
Posted by justaguide on June 2, 2011 at 12:26 PM (Answer #2)
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