Verified answer

[tex]f(x) = \sqrt{3x + 1} \\ f'(x)-? \\ f'(x) = \frac{1}{2 \sqrt{3x + 1} } \times (3x + 1)' = \\ = \frac{1}{2 \sqrt{3x + 1} } \times ((3 \times (x)' + (1)') = \\ \\ = \frac{1}{2 \sqrt{3x + 1} } \times (3 \times 1 + 0) = \\ = \frac{3}{2 \sqrt{3x + 1} } \\ f'(x) = \frac{3}{2 \sqrt{3x + 1} } [/tex]