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

Show that the function f(x)={x^msin(1/x),\ \ \ x!=0 , 0\ \ x=0 is differentiable at x=0 , if (m>1)

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

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

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 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^msin(1/x), x=0 ,0 ,\ \ \ x!=0 ,\ \ \ \ \ \ \x=0 is differentiable at x=0 , if m >1

Show that the function f (x) = (x)/(1 + |x| ) , x in R, is differentiable at x =0. Hence find f '(0).