AI engineering glossary · Calculus optimisation
What is differentiability?
Differentiability: A function is differentiable at a point if its slope exists and is the same whether you approach from the left or the right. Sharp corners, jumps and vertical tangents break it. Deep-learning frameworks still handle non-smooth points, such as ReLU at zero, by choosing a convention.
Differentiability: an example
f(x) = |x| is continuous but not differentiable at x = 0 because the slope is -1 on the left and +1 on the right.
Related terms
More Calculus optimisation terms
- Directional derivative
- Duality
- Euler's number
- Exponential function
- Feasible region
- Finite difference
- First-order condition
- Flat minimum
Where you learn it
Differentiability is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.