The set of points where  is differentiable, is:

Concept:

• Differentiability of a Function: A function f(x) is differentiable at x = a in its domain if its derivative is continuous at a.

  This means that f'(a) must exist, or equivalently: .

• The Modulus Function '| |' is defined as: .

Calculation:

By using the definition of modulus function, the given function can be written as: .

Since the expressions for f(x) change for x > 0 and x < 0, let us compare the limits of the derivatives as x → 0.

For x > 0, .

⇒

⇒ 

⇒ 

⇒ .

Similarly, for x < 0, .

⇒ .

Since , the function f(x) is differentiable at x = 0, and f'(0) = 1.

Also, .

∴ The function is differentiable in (-∞, ∞), i.e. it is differentiable everywhere.