Mathematical formulas

Differential Calculus

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Sections

1Notation, functions and domains
2Limits
3Continuity
4Derivative and geometric interpretation
5Differentiation rules
6Higher-order derivatives
7Mean value theorem
8Function analysis
9Optimization
10Linear approximations and differentials
11Taylor series (introduction)
12L'Hôpital and indeterminate limits
13Implicit and related functions
14Related rates
15Graphs and asymptotic behavior
16Guide to differentiate and analyze
AAppendix A: extended derivative table

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Differential Calculus
Basic rules
Formula

5.1. Basic rules

Formula

In 5.1. Basic rules

Formula

\frac{d}{dx}[x^n]=nx^{n-1},\qquad n\in\mathbb{R},\ x>0\ \text{if }n\notin\mathbb{Z}

Tags

Differential calculus
Derivative
Derivative formula
Rule
Basic rules

Detail

For non-integer

n\in\mathbb{R}

, valid on each interval where

x>0

(or where

x^n

is defined and differentiable).

Variables

$x$ Independent variable
$f'$ Derivative of $f$
$n$ Derivative order or exponent
$dx$ Differential of $x$

Conditions

$n\in\mathbb{R},\ x>0\ \text{if }n\notin\mathbb{Z}$

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