Question

Question #5c275

Answer 1

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

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)`