find the valu of local extremum for f(x)=sin x-cos x,0<x<2∏.
Kind of a basic problem isn't it? Can you find the derivative of f(x)?
Looks like homework to me so I am going to move it.
I will also point out that, because there is only the single independent variable, x, there is NO "partial differentiation" here.
Separate names with a comma.