Answer
$f'(x)=\dfrac{5}{2\sqrt{5x+1}}$
Work Step by Step
$f(x)=\sqrt{5x+1}$
Let's write the function like this:
$f(x)=(5x+1)^{1/2}$
Differentiate using the chain rule:
$f'(x)=\dfrac{1}{2}(5x+1)^{-1/2}(5x+1)'=...$
$...=\dfrac{1}{2}(5x+1)^{-1/2}(5)=\dfrac{5}{2}(5x+1)^{-1/2}=\dfrac{5}{2(5x+1)^{1/2}}=...$
$...=\dfrac{5}{2\sqrt{5x+1}}$
