# Can you differentiate a complex function?

Table of Contents

## Can you differentiate a complex function?

We can differentiate complex functions of a real parameter in the same way as we do real functions. If w(t) = f(t) + ig(t), with f and g real functions, then w'(t) = f'(t) + ig'(t). The basic derivative rules still work.

## What does it mean for a complex function to be real differentiable?

A real function f(x) is said to be differentiable at x0, an interior point of its domain, if. the ratio of ∆f = f(x) − f(x0) to ∆x = x − x0 has a limit as ∆x → 0 ∶ lim. ∆x→0. ∆f.

**Is the complex conjugate function differentiable?**

Conjugation is a reflection so it flips orientation, therefore it cannot be differentiable at any point in the complex sense.

**What is the derivative of a complex number?**

The notion of the complex derivative is the basis of complex function theory. The definition of complex derivative is similar to the derivative of a real function. However, despite a superficial similarity, complex differentiation is a deeply different theory. f′(z0)=limz→z0f(z)−f(z0)z−z0.

### How do you prove that a function is differentiable at a point?

- Lesson 2.6: Differentiability: A function is differentiable at a point if it has a derivative there.
- Example 1:
- If f(x) is differentiable at x = a, then f(x) is also continuous at x = a.
- f(x) − f(a)
- (f(x) − f(a)) = lim.
- (x − a) · f(x) − f(a) x − a This is okay because x − a = 0 for limit at a.
- (x − a) lim.
- f(x) − f(a)

### Is differentiability the same as differentiation?

Differentiability refers to the existence of a derivative while differentiation is the process of taking the derivative. So we can say that differentiation of any function can only be done if it is differentiable.

**Is Derivability and differentiability same?**

In french, the quality of a function which in english is called ‘differentiable’, we call ‘dérivable’. And we call ‘différentiable’ at the point (x,y) a function f such that we can write f(x+h,y+k) – f(x,y) = h*df(x,y)/dx + k*df(x,y)/dy + o(sqrt{h²+k²}).