## Calculus 8th Edition

f'(x) = $\frac{5}{2}(5x + 1)^{-1/2}$
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) = $\frac{5}{2}(5x + 1)^{-1/2}$