# Category:Differential Calculus

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This category contains results about **Differential Calculus**.

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

**Differential calculus** is the subfield of calculus which is concerned with the study of the rates at which quantities change.

## Also see

## Subcategories

This category has the following 43 subcategories, out of 43 total.

### C

- Cauchy Mean Value Theorem (6 P)

### D

- Derivative of Arc Length (3 P)
- Derived Equations (empty)

### E

- Extended Mean Value Theorem (5 P)

### F

- Faà di Bruno's Formula (14 P)

### I

- Inverse Function Theorem (3 P)

### J

- Jacobian Determinants (empty)

### L

- Leibniz's Rule (13 P)

### M

### P

### Q

### R

- Rate of Change (empty)

### S

- Sum Rule for Derivatives (4 P)

## Pages in category "Differential Calculus"

The following 86 pages are in this category, out of 86 total.

### C

### D

- Derivative at Maximum or Minimum
- Derivative Function is not Invertible
- Derivative Function on Set of Functions induces Equivalence Relation
- Derivative iff Right and Left Derivative
- Derivative of Arc Length
- Derivative of Composite Function
- Derivative of Curve at Point
- Derivative of Even Function is Odd
- Derivative of Function plus Constant
- Derivative of Function to Power of Function
- Derivative of Geometric Sequence
- Derivative of Geometric Sequence/Corollary
- Derivative of Inverse Function
- Derivative of Monotone Function
- Derivative of Odd Function is Even
- Derivative of Periodic Real Function
- Derivative of Power of Function
- Derivative of Scalar Triple Product of Vector-Valued Functions
- Derivative of Strictly Increasing Real Function is Strictly Positive
- Derivative of Uniformly Convergent Sequence of Differentiable Functions
- Derivative of Uniformly Convergent Series of Continuously Differentiable Functions
- Derivative of Vector Triple Product of Vector-Valued Functions
- Derivatives of Function of a x + b
- User:Dezhidki/Sandbox
- Differentiability of Function with Translation Property
- Differentiable Bounded Concave Real Function is Constant
- Differentiable Bounded Convex Real Function is Constant
- Differentiation of Real Power Series
- Differentiation of Real Power Series/Corollary
- Differentiation of Vector-Valued Function Componentwise
- Differentiation on Polynomials is Linear Operator
- Dot Product of Constant Magnitude Vector-Valued Function with its Derivative is Zero
- Dot Product of Vector-Valued Function with its Derivative
- Double Root is Root of First Derivative of Equation but not Second Derivative

### E

- Epsilon-Function Differentiability Condition
- Equivalence Classes induced by Derivative Function on Set of Functions
- Equivalence of Definitions of Derivative
- Even Order Derivative of Odd Function Vanishes at Zero
- Exponential Function is Differentiable
- Extendability Theorem for Derivatives Continuous on Open Intervals
- Extended Mean Value Theorem

### L

### M

### N

### P

### R

- Real Function is Concave iff Derivative is Decreasing
- Real Function is Convex iff Derivative is Increasing
- Real Function is Strictly Concave iff Derivative is Strictly Decreasing
- Real Function is Strictly Convex iff Derivative is Strictly Increasing
- Real Function with Negative Derivative is Decreasing
- Real Function with Positive Derivative is Increasing
- Real Function with Strictly Negative Derivative is Strictly Decreasing
- Real Function with Strictly Negative Second Derivative is Strictly Concave
- Real Function with Strictly Positive Derivative is Strictly Increasing
- Real Function with Strictly Positive Second Derivative is Strictly Convex
- Right-Hand Derivative not Limit of Derivative from Right

### S

- Second Derivative at Point of Inflection
- Second Derivative of Concave Real Function is Non-Positive
- Second Derivative of Convex Real Function is Non-Negative
- Slope of Curve at Point equals Derivative
- Subspace of Real Differentiable Functions
- Sum Rule for Derivatives
- Sum Rule for Derivatives/General Result