if f `(x) = x^3`, show that f''(x) exist for all real values of x and find it.

Show that f(x) = x-[x] is discontinuous for integral values of x

If f(x)=x^(x) , then find f'(x) .

If f(x)=(2x+1)/(3x-2)=y ,show that x=f(y).

Consider d : R to R given by f (x) = 4x + 3. Show that f is invertible . Also , find the inverse of f.

If f(x)=sin x^(o) , then find f' (x).

Show that f (x) = |x| is continuous at x= 0 but f'(0) does not exist

If f(x)=(x-1)/(x+1) ,then show that f(1/x)=-f(x) .

If f(x)=x|x| , then find f'(0).

Show that f(x)=e^(1//x) is a strictly decreasing function for all x in R .

Let f : R rarr R be defined as f(x)=x^3+2 . Show that f^-1 : R rarr R exists and hence find the formula for f^-1 .