<    1    >

---

Differentiable

The function f (x) is differentiable in x = a if the derivate f ′(a) exists, where . These conditions are required and sufficient.

 

---

Explanation

The derivative of f (x) is defined as both limits from the left and from right to the point x = a

     and     

for h > 0.

 

---

Example 1

The lateral derivatives of the function f (x) = |x| in x = 0 are

This function cannot be differentiated at this point, as the tangent lines from left and from right are not equal.

 

---

Deutsch   Español   Français   Nederlands   中文   Русский