What is the first derivative of the function x*sinx+cosx ?

We'll differentiate the function with respect to
x.

We'll note the function as y =
f(x):

dy/dx = d/dx(x)*sinx + x*d/dx(sin x) +
d/dx(cosx)

dy/dx = sin x + x*cosx - sin
x

We'll eliminate like
terms

dy/dx = x*cosx

The first
derivative of the function f(x) is:

f'(x) =
x*cos x