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)="x"|"x"|

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|)

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,

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

Let f(x)=(x^(2)-3x+2)|(x^(3)-6x^(2)+11x-6)|+|sin(x+(pi)/(4))| Number of points at which the function f(x) is non-differentiable in [0,2 pi], is

A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all x ,\ y in R , f(x)!=0 . Suppose that the function f(x) is differentiable at x=0 and f^(prime)(0)=2 . Prove that f^(prime)(x)=2\ f(x) .

A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all x ,\ y in R , f(x)!=0 . Suppose that the function f(x) is differentiable at x=0 and f^(prime)(0)=2 . Prove that f^(prime)(x)=2\ f(x) .