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2: Differentiation

Last updated

Jun 11, 2024
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- 1.7: Extra Problems for Chapter 1
- 2.1: Derivatives

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2.1: Derivatives
Derivative as the standard part of the slope of a hyperreal straight line through a point on a curve. Examples of how to calculate derivative and how the concept can be applied to contexts such as velocity and marginal values.
2.2: Differentials and Tangent Lines
Finding the tangent line to a curve at a given point. Using the tangent line as the basis for differentials of independent and dependent variables.
2.3: Derivatives of Rational Functions
Differentiating rational functions, with discussion and proofs of the Constant, Sum, Product, Quotient, and Power Rules.
2.4: Inverse Functions
Definition of inverse functions. The Inverse Function Rule for finding the derivative of a function using the derivative of its inverse.
2.5: Transcendental Functions
Definitions and derivatives of the trigonometric, exponential and logarithmic functions.
2.6: Chain Rule
Defining compositions of functions. Using the Chain Rule to differentiate compositions of functions and functions of dependent variables.
2.7: Higher Derivatives
Definition of higher-order derivatives of a function, and how to calculate them.
2.8: Implicit Functions
Definition of implicit functions and rules of implicit differentiation.
2.9: Extra Problems for Chapter 2

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