Which of the function is non-differential at `x=0?` `f(x)="x"|"x"|`

Which of the function is non-differential at x=0? f(x)=|"x"^3|

Which of the function is non-differential at x=0? f(x)="cos"|x|

Which of the following function is not differentiable at x=0? f(x)={(0 ,, xgeq0),(x^2 ,, x<0):} , f(x)=x^2sgn(x)

Which of the following function is non-differentiable in domain? f(x)=(x-2)/(x^2+3) (b) f(x)=log|x| f(x)=x^3logx (d) f(x)=(x-3)^(3/5)

Prove the each of the following function is differentiable at x=0. (i) f(x) = cos|x| (ii) f(x) = x|x| (iii) f(x)=|x^(3)|(iv) f(x) =(x)/(1+|x|)

Show that f(x)=|x| is not differentiable at x=0.

Show that f(x)=|x| is not differentiable at x=0 .

Show that the function f(x)=x^(3/2) is not differentiable at x=0.

A function f : R rarr R satisfies the equation f(x + y) = f(x) . f(y) for all, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2. Then,

A function f : R rarr R satisfies the equation f(x+y) = f(x). f(y) for all x y in R, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2 , then prove that f' = 2f(x) .