We have the function f(x) = x*cos x + sin (-x)

f(x) = x*cos x - sin x

The first derivative of f(x) is f'(x)

=> f'(x) = cos x - x*(sin x) - cos x

=> f'(x) = -x*sin x

When 0< x< 180 we have sin x as...

## Unlock

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

We have the function f(x) = x*cos x + sin (-x)

f(x) = x*cos x - sin x

The first derivative of f(x) is f'(x)

=> f'(x) = cos x - x*(sin x) - cos x

=> f'(x) = -x*sin x

When 0< x< 180 we have sin x as positive, therefore the first derivative -x*sin x is negative, so the function is decreasing.

**Therefore the function is decreasing for the given range of x.**