Answer
f'(x) = $\frac{5}{2}(5x + 1)^{-1/2}$
Work Step by Step
To find the derivative of f(x), we can first realize that $\sqrt(5x + 1)$ is the same thing as $(5x + 1)^{1/2}$
From there we need to identify the inside and outside functions.
The inside function is 5x + 1
The outside function is $u^{1/2}$
We know from the chain rule that f'(x) will be equal to the derivative of the outside function multiplied by the inside function:
f'(x) = $\frac{1}{2}(5x + 1)^{-1/2}(5)$
which is the same thing as
f'(x) = $\frac{5}{2}(5x + 1)^{-1/2}$
