I'm assuming
[tex]f(x)=\dfrac x{\cot x+3}[/tex]
By the quotient rule, the derivative [tex]f'(x)[/tex] is
[tex]\dfrac{(\cot x+3)(x)'-x(\cot x+3)'}{(\cot x+3)^2}=\dfrac{(\cot x+3)(1)-x(-\csc^2x)}{(\cot x+3)^2}=\dfrac{x\csc^2x+\cot x+3}{(\cot x+3)^2}[/tex]
