For the function ` f(x) =\frac ( 2 tan x )( x ) `, you need to apply the quotient rule to find `f′(x)`. The quotient rule states that for a function in the form `\frac{u}{v}`, the derivative `f'(x)` is given by: `f'(x) = \frac{v \cdot u' - u \cdot v'}{v^2}`. Here, `u=2 tan x` and `v=x`. Differentiate `u` and `v` separately using the standard rules for differentiation, and then apply the quotient rule formula to find `f'(x)`. Once you find f'( x ) ` subsititue `x= 4` and solve.