[tex]g(x)=4x-\dfrac{1}{4x}=4x-(4x)^{-1}\\\\\\\\g'(x)=\left[4x-(4x)^{-1}\right]'=(4x)'-\left[(4x)^{-1}\right]'=4-[-1(4x)^{-2}]\cdot4\\\\=4+\dfrac{1}{(4x)^2}\cdot4=4+\dfrac{4}{4^2x^2}=\boxed{4+\dfrac{1}{4x^2}}\\\\Used:\\\\(f(x)-g(x))'=f'(x)-g'(x)\\\\.[f(g(x))]'=f'(g(x))\cdot g'(x)\\\\(x^n)'=nx^{n-1}[/tex]
