[tex] \large \bold{SOLUTION:} [/tex]
[tex] \begin{array}{l} \bold{Given:}\:\sf y=\sqrt{3x^2 + 5x - 8} \\ \\ \bold{Required:}\:\sf y' \textsf{ at }x = 2\\ \\ \sf y' = \dfrac{dy}{dx} = \dfrac{d}{dx} (3x^2 + 5x - 8)^{\frac{1}{2}} \\ \\ \sf y' = \dfrac{1}{2}(3x^2 + 5x - 8)^{-\frac{1}{2}}(6x + 5) \\ \\ \sf y' = \dfrac{6x + 5}{2\sqrt{3x^2 + 5x - 8}} \\ \\ \sf \textsf{At }x = 2, \\ \\ \sf y' = \dfrac{6(2) + 5}{2\sqrt{3(2)^2 + 5(2) - 8}} \\ \\ \boxed{\sf y' = \dfrac{17}{2\sqrt{14}} \textsf{ or approx. } 2.2717} \end{array} [/tex]
