Mathematical formulas

Differential Calculus

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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
Physical interpretation
Formula

4.3. Physical interpretation

Formula

In 4.3. Physical interpretation

Formula

a(t)=v'(t)=s''(t)

Tags

Differential calculus
Derivative
Physical interpretation
Derivative formula

Detail

Instantaneous acceleration.

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Explore the idea

Variables

$t$ Time (physical interpretation)
$s$ Position or arc length
$v$ Velocity or auxiliary function
$a$ Point or real constant

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Related formulas

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Instantaneous acceleration
$a=\frac{dv}{dt}=\frac{d^2x}{dt^2}$
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Related
Formula
$v(t)=s'(t)$
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