The chain rule gives
f ′ ( x ) = 1 5 x ⋅ 1 2 5 x ⋅ 5 = 1 2 x {\displaystyle f'(x)={\frac {1}{\sqrt {5x}}}\cdot {\frac {1}{2{\sqrt {5x}}}}\cdot 5={\frac {1}{2x}}} .
Thus
f ′ ( 1 5 ) = 1 2 ⋅ 1 5 = 5 2 {\displaystyle f'({\frac {1}{5}})={\frac {1}{2\cdot {\frac {1}{5}}}}={\frac {5}{2}}} .