# Category:Definitions/Differentials

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This category contains definitions related to Differentials.

Related results can be found in **Category:Differentials**.

### Real Function

Let $U \subset \R$ be an open set.

Let $f: U \to \R$ be a real function.

Let $f$ be differentiable at a point $x \in U$.

The **differential of $f$ at $x$** is the linear transformation $\map {\d f} x : \R \to \R$ defined as:

- $\map {\map {\d f} x} h = \map {f'} x \cdot h$

where $\map {f'} x$ is the derivative of $f$ at $x$.

## Subcategories

This category has only the following subcategory.

### D

## Pages in category "Definitions/Differentials"

The following 18 pages are in this category, out of 18 total.

### D

- Definition:Differential of Mapping
- Definition:Differential of Mapping/Functional
- Definition:Differential of Mapping/Manifolds
- Definition:Differential of Mapping/Notation
- Definition:Differential of Mapping/Real Function
- Definition:Differential of Mapping/Real Function/Open Set
- Definition:Differential of Mapping/Real Function/Point
- Definition:Differential of Mapping/Real-Valued Function
- Definition:Differential of Mapping/Real-Valued Function/Point
- Definition:Differential of Mapping/Vector-Valued Function
- Definition:Differential of Mapping/Vector-Valued Function/Point
- Definition:Differential of Mapping/Warning
- Definition:Differential of Real Function
- Definition:Differential of Real Function at Point
- Definition:Differential of Real-Valued Function
- Definition:Differential of Vector-Valued Function
- Definition:Differential of Vector-Valued Function at Point
- Definition:Differential Operator