Prove that `f(x)={x sin (1/x), x != 0, 0,x=0` is not differentiable at `x=0.`

Show that the function f(x)={x^m sin(1/x) , 0 ,x != 0,x=0 is differentiable at x=0 ,if m > 1 and continuous but not differentiable at x=0 ,if 0

Prove that f(x) = x^(3)+3 if x!=0 and 1 if x=0 is not differentiable at x = 0.

Prove that the function f(x)={x/(1+e^(1/x)); if x != 0 0; if x=0 is not differentiable at x = 0.

Show that the function f(x)={x^(m)sin((1)/(x))0,x!=0,x=0 is differentiable at x=0 if m>1 continuous but not differentiable at x=0, if 0.

Show that the function f(x)={((x^2sin(1/x),if,x!=0),(0,if,x=0)) is differentiable at x=0 and f'(0)=0

Show that the function f(x)={((x^2sin(1/x),if,x!=0),(0,if,x=0)) is differentiable at x=0 and f'(0)=0

Show that the function f(x)={ x^2sin(1/x) , when x !=0 and 0 when x=0 } is differentiable at x=0.

Let f(x) ={{:(sqrt(x)(1+x sin (1//x)), xgt0),( - sqrt((-x))(1+ sin (1//x)), x lt 0),( 0, x=0):} Discuss differentiability at x=0.

Show that the functions f (x) = x ^(3) sin ((1)/(x)) for x ne 0, f (0) =0 is differentiable at x =0.

Show that the function f(x)={x^(2)sin((1)/(x)),whenx!=0 and 0 whenx =0} is differentiable at x=0