# What is the derivative of absolute function?

## What is the derivative of absolute function?

Derivative of an Absolute Value Function Use the chain rule of differentiation to find the derivative of f=|u(x)|=√u2(x).

## Can you take derivative of complex number?

If f = u + iv is a complex-valued function defined in a neigh- borhood of z ∈ C, with real and imaginary parts u and v, then f has a complex derivative at z if and only if u and v are differentiable and satisfy the Cauchy- Riemann equations (2.2. 10) at z = x + iy. In this case, f′ = fx = −ify.

**Why is an absolute value function not differentiable?**

The left limit does not equal the right limit, and therefore the limit of the difference quotient of f(x) = |x| at x = 0 does not exist. Thus the absolute value function is not differentiable at x = 0.

**Does a derivative of an absolute value function exist?**

The absolute value function has a derivative(s) on restricted domains. i.e. f'(x) = -1 for x <0 and f'(x) = 1 for x > 0. However, the absolute value function is not “smooth” at x = 0 so the derivative at that point does not exist. The power rule only applies to power functions.

### What is the absolute value of 4i?

Expert Answer The absolute value of the number 4i is 4.

### How do you check whether the function is differentiable or not?

A function is formally considered differentiable if its derivative exists at each point in its domain, but what does this mean? It means that a function is differentiable everywhere its derivative is defined. So, as long as you can evaluate the derivative at every point on the curve, the function is differentiable.

**Can an absolute value function be differentiable?**

**Is absolute value holomorphic?**

As a consequence of the Cauchy–Riemann equations, any real-valued holomorphic function must be constant. Therefore, the absolute value | z |, the argument arg (z), the real part Re (z) and the imaginary part Im (z) are not holomorphic.