Show that `f(x)=x^2` is differentiable at `x=1` and find `f^(prime)(1)` .

Show that f(x)=x^(2) is differentiable at x=1 and find f(1)

Show that f(x)=x^(2) is differentiable at x=1 and find f'(1)

Show that f(x)=x^(2) is differentiable at x=1 and find f'(1) .

Show that f (x) = 2x +3 is differentiable at x=1 and hence find f'(1).

Show that f (x) = [x] is not differentiable at x = 1 .

Show that f(x)=(x-1)^((1)/(3)) is not differentiable at x=1

Suppose that f(x) is differentiable invertible function f^(prime)(x)!=0a n dh^(prime)(x)=f(x)dot Given that f(1)=f^(prime)(1)=1,h(1)=0 and g(x) is inverse of f(x) . Let G(x)=x^2g(x)-x h(g(x))AAx in Rdot Which of the following is/are correct? G^(prime)'(1)=2 b. G^(prime)'(1)=3 c. G^(prime)(1)=2 d. G^(prime)(1)=3

If f(x) is differentiable at x=a and f^(prime)(a)=1/4dot Find (lim)_(h->0)(f(a+2h^2)-f(a-2h^2))/(h^2)

Show that f(x)={12 x-13 ,\ \ \ if\ xlt=3 \ \ \ \ \ 2x^2+5,\ \ \ \ \ if\ x >3 is differentiable at x=3 . Also, find f^(prime)(3) .

Show that, the function f(x) = |x-1| is not differentiable at x = 1