Question #5c275

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Answer 1 · 2017-05-15T01:00:26

#dy/dx=4pi+(1/2)#

#dy/dx=x(cos^2(x))'+(cos^2(x))(x)'#

We will need to use the chain rule to find the derivative of #cos^2(x))#:

#dy/dx=-x(2cos(x)sin(x))+cos^2x#

Plug in #pi/4#

#dy/dx=-(pi/4)(2cos(pi/4)sin(pi/4))+cos^2(pi/4)#

This becomes:

#dy/dx=-(pi/4)(2(sqrt(2)/2)(sqrt(2)/2))+(2/4)#

Evaluate:

#dy/dx=-pi/4+(1/2)#