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:

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