Question

If f(x)=(x-1)^(3/2) +((e^(x-2))/2), then f'(2)=

Answer 1

`f(x) = (x - 1)^{(3)/(2)} + (e^(x - 2))/(2)`

`f(2) = (2 - 1)^{(3)/(2)} + (e^(2 - 2))/(2)`

`f(2) = (1)^{(3)/(2)} + (e^(0))/(2)`

`f(2) = 1 + (1)/(2)`

`f(2) = 1(1)/(2)`


`f'(x) = \frac{3(x - 1)^{(1)/(2)} + e^(x - 2)}{2}`

`f'(2) = \frac{3(2 - 1)^{(1)/(2)} + e^(2 - 2)}{2}`

`f'(2) = \frac{3(1)^{(1)/(2)} + e^(0)}{2}`

`f'(2) = (3(1) + 1)/(2)`

`f'(2) = (3 + 1)/(2)`

`f'(2) = (4)/(2)`

`f'(2) = 2`