Calculus of a Single Variable, Chapter 2, 2.3, Section 2.3, Problem 50

Note:- 1) If y = sinx ; then dy/dx = cosx
2) If y = cosx ; then dy/dx = -sinx
3) If y = u*v; where 'u' & 'v' are functions of 'x' ; then dy/dx = uv' + vu'
Now,
y = xsinx + cosx
dy/dx = y' = xcosx + sinx - sinx
or, dy/dx = y' = xcosx