Question #5c275

1 Answer
May 15, 2017

dy/dx=4pi+(1/2)dydx=4π+(12)

Explanation:

Use product rule :

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)