[tex]f(x) = (x - 1)^{\frac{3}{2}} + \frac{e^{x - 2}}{2}[/tex]
[tex]f(2) = (2 - 1)^{\frac{3}{2}} + \frac{e^{2 - 2}}{2}[/tex]
[tex]f(2) = (1)^{\frac{3}{2}} + \frac{e^{0}}{2}[/tex]
[tex]f(2) = 1 + \frac{1}{2}[/tex]
[tex]f(2) = 1\frac{1}{2}[/tex]
[tex]f'(x) = \frac{3(x - 1)^{\frac{1}{2}} + e^{x - 2}}{2}[/tex]
[tex]f'(2) = \frac{3(2 - 1)^{\frac{1}{2}} + e^{2 - 2}}{2}[/tex]
[tex]f'(2) = \frac{3(1)^{\frac{1}{2}} + e^{0}}{2}[/tex]
[tex]f'(2) = \frac{3(1) + 1}{2}[/tex]
[tex]f'(2) = \frac{3 + 1}{2}[/tex]
[tex]f'(2) = \frac{4}{2}[/tex]
[tex]f'(2) = 2[/tex]
