There are two likely interpretations for the given function:
[tex]f(x)=7x^3+\dfrac x{6\sqrt x}[/tex]
in which case you can write
[tex]\dfrac x{6\sqrt x}=\dfrac x{6x^{1/2}}=\dfrac16x^{1/2}[/tex]
and the derivative is
[tex]f'(x)=21x^2+\dfrac1{12}x^{-1/2}=21x^2+\dfrac1{12\sqrt x}[/tex]
Or, perhaps it is
[tex]f(x)=\dfrac{7x^3+x}{6\sqrt x}=\dfrac76x^{5/2}+\dfrac16x^{1/2}[/tex]
[tex]\implies f'(x)=\dfrac{35}{12}x^{3/2}+\dfrac1{12\sqrt x}[/tex]
