## Is Lnx differentiable?

The function lnx is differentiable and continuous on its domain (0,с), and its derivative is d dx lnx = 1 x . function is continuous, therefore lnx is continuous.

### How do you check a function is infinitely differentiable?

The function f is said to be infinitely differentiable, smooth, or of class C∞, if it has derivatives of all orders. The function f is said to be of class Cω, or analytic, if f is smooth and if its Taylor series expansion around any point in its domain converges to the function in some neighborhood of the point.

#### Where is Lnx not differentiable?

The derivative of f is ln|x|+1 and is defined for x≠0. The function is not differentiable at 0, however the derivative is continuous on its domain of definition.

**What is the meaning of infinitely differentiable?**

in most situations, infinitely differentiable means that you are allowed to differentiate the function as many times as you wish, since these derivatives exist (everywhere). The value of the derivatives is irrelevant, of course.

**What does infinitely differentiable mean and what is an example of an infinitely differentiable function?**

An infinitely differentiable function is a function in which derivatives of all orders exist. For example, let f(x)=sin(x), then f'(x)=cos(x), f”(x)=-sin(x), f”'(x)=-cos(x), and f^(4)(x)=sin(x). Thus the fifth derivative will start the cycle over again, and it will repeat infinitely. Another example is g(x)=e^x.

## How do you prove that a function is C infinity?

A function is C1 if its derivative is continuous. A function is C-infinity if derivatives of all order are continuous.

### Are logs continuous?

The natural logarithm function is continuous.

#### Is a constant function infinitely differentiable?

Yes. f′ and all higher derivatives are identically equal to zero.

**Is 0 continuously differentiable?**

Yes. Zero is a constant, and constants are differentiable. The derivative of any constant is zero, e.g.