f(x) = sqrt ( x^2 + (4x/x - 8)^2 )
thanks a lot for you help
What have you tried yourself? If you let $\displaystyle u= x^2$, $\displaystyle v= \frac{4x}{x- 8}$, and $\displaystyle w= v^2$, that function is $\displaystyle f(x)= (u+ v)^{1/2}$
You will need to use the power rule, the quotient rule, and the chain rule.