# Category:Derivatives

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This category contains results about **Derivatives** in the context of **Differential Calculus**.

Definitions specific to this category can be found in **Definitions/Derivatives**.

Let $I \subset \R$ be an open interval.

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

Let $f$ be differentiable on the interval $I$.

Then the **derivative of $f$** is the real function $f': I \to \R$ whose value at each point $x \in I$ is the derivative $\map {f'} x$:

- $\ds \forall x \in I: \map {f'} x := \lim_{h \mathop \to 0} \frac {\map f {x + h} - \map f x} h$

## Subcategories

This category has the following 15 subcategories, out of 15 total.

## Pages in category "Derivatives"

The following 35 pages are in this category, out of 35 total.

### D

- Derivative of Absolute Value Function
- Derivative of Absolute Value Function/Corollary
- Derivative of Constant
- Derivative of Constant Multiple
- Derivative of Cosine Integral Function
- Derivative of Error Function
- Derivative of Exponential Integral Function
- Derivative of Fresnel Cosine Integral Function
- Derivative of Fresnel Sine Integral Function
- Derivative of Function of Constant Multiple
- Derivative of Gamma Function
- Derivative of Gaussian Hypergeometric Function
- Derivative of Identity Function
- Derivative of Identity Function/Corollary
- Derivative of Identity Function/Real
- Derivative of Matrix Exponential
- Derivative of Nth Root
- Derivative of Power
- Derivative of Power of Constant
- Derivative of Riemann Zeta Function
- Derivative of Sine Integral Function
- Derivative of Square Function
- Derivatives of Function of a x + b
- Derivatives of Hyperbolic Functions
- Derivatives of Inverse Trigonometric Functions
- Derivatives of Real Area Hyperbolic Functions
- Derivatives of Trigonometric Functions