Answer:
[tex]g'(x)=cos (x)-xsin(x)[/tex]
Step-by-step explanation:
If g(x)=x cos (x)
We want to determine the derivative of g(x).
Using Product rule: [tex]{\left( {u\,v} \right)^\prime } = u'\,v + u\,v'[/tex]
[tex]u=x : u'=1\\v=cos (x): v'=-sin(x)[/tex]
Therefore:
[tex]g'(x)=cos (x)+x(-sin(x))\\g'(x)=cos (x)-xsin(x)[/tex]
