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Calculus volume 1
Derivatives
Derivatives
OpenStax
@
Introduction
Defining the derivative
1
Tangent lines
2
The derivative of a function at a point
3
Velocities and rates of change
4
Key concepts
5
Key equations
The derivative as a function
1
Derivative functions
2
Graphing a derivative
3
Derivatives and continuity
4
Proof
5
Higher-order derivatives
6
Key concepts
7
Key equations
Differentiation rules
1
The basic rules
2
The constant rule
3
The power rule
4
Proof
5
The sum, difference, and constant multiple rules
6
Proof
7
The product rule
8
Proof
9
The quotient rule
10
Proof
11
Combining differentiation rules
12
Key concepts
Derivatives as rates of change
1
Amount of change formula
2
Motion along a line
3
Population change
4
Changes in cost and revenue
5
Key concepts
Derivatives of trigonometric functions
1
Derivatives of the sine and cosine functions
2
Proof
3
Derivatives of other trigonometric functions
4
Higher-order derivatives
5
Key concepts
6
Key equations
The chain rule
1
Deriving the chain rule
2
The chain and power rules combined
3
Combining the chain rule with other rules
4
Composites of three or more functions
5
Proof
6
The chain rule using leibniz’s notation
7
Key concepts
8
Key equations
Derivatives of inverse functions
1
The derivative of an inverse function
2
Proof
3
Derivatives of inverse trigonometric functions
4
Key concepts
5
Key equations
Implicit differentiation
1
Implicit differentiation
2
Finding tangent lines implicitly
3
Key concepts
Derivatives of exponential and logarithmic functions
1
Derivative of the exponential function
2
Derivative of the logarithmic function
3
Proof
4
Proof
5
Logarithmic differentiation
6
Key concepts
7
Key equations
8
Chapter review exercises
Source:
OpenStax, Calculus volume 1. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11964/1.2
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