if f(x)={1-x^2, x< or = -1 and 2x+2 , x>-1},then the derivative of f(x) at x= -1 is

LHL of f(x) = 0; RHL of f(x) = 0    so, f(x) is continous

now,

f^'(x)=  -2x   for x<=-1

           2     for  x>-1

left hand derivative at x= -1 is 2 and right hand derivative is =2

so, LHD=RHD

so f^'(x=-1) is = 2.