Does f'(1) exist if `f(x) = |x-1|+|x+1|`

Find from the definition of derivative: )f'(1)if f(x) = x^2-2x + 3

Find f {f (x)} if f(x)=(x+1)/(x-1)

Prove that f (x) = |x-1|,x in R is not differnentiable at x=1

find the points of discontinuity of the function f defined by f(x) = {(x^3 - 3, x le 2),(x^2 + 1, x > 2):}

Find the domain and range of f if . f(x)=|x+1|/(x+1)

Find f'(x), if f(x)= tan^(-1) ""sqrt((1-cos2x)/(1+cos2x))

If alpha,beta are the zeroes of the polynomial f(x)=x^2+x+1 then 1/alpha+1/beta is____