we are given the function f(x)=sqrt of (4sinx+2) and is asked to find the first derivative of the function when x is equal to zero.
f(x)=sqrt of (4sinx+2)
f'(x) = 0.5 (4sinx+2) ^ -0.5 * (4cosx)
f'(0) = 0.5 (4sin0+2) ^ -0.5 * (4cos0)
f'(0) = 0.5 (0+2) ^ -0.5 * (4*1)
f'(x) = 0.5 (2) ^ -0.5 * (4)
f'(x) = -.1.65