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Basic rules of derivative

Basic rules of derivative preview
Basic rules of derivative preview
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Look Inside · 10 pages

Opening slide introduces basic derivative rules and the objective of using them to differentiate functions.
Opening slide of the differentiation lesson
Derivative lesson slide defines differentiability, links it to continuity, and shows alternate notation.
Definitions and notation for derivatives
Lesson introduction explains why derivative rules help and identifies constant and power functions as basics.
Introduction to rules for differentiation
Constant rule derivation uses the limit definition to show that f(x) = k has derivative zero and slope zero.
Deriving the constant rule from a limit
Constant rule theorem states that the derivative of k is zero; worked Example 1 applies it to f(x) = 4.
Constant rule theorem and worked Example 1
Constant rule lesson slide repeats the theorem and applies it to f(x) = -7 in worked Example 2, giving zero.
Worked Example 2: a negative constant
Power rule development derives the derivative of x cubed as 3x squared using expansion and a limit.
Deriving the derivative of x cubed
Power rule development derives the derivative of x to the fourth as 4x cubed using the limit definition.
Deriving the derivative of x to the fourth
Power rule lesson slide generalizes derivatives of powers and applies the rule to x^12 in worked Example 3.
Power rule statement and worked Example 3
Power rule worked Example 4 rewrites 1/x^3 as x^-3 and differentiates it to obtain -3/x^4 step by step.
Worked Example 4: a negative exponent
Attributes
Subject

Math, Calculus

Grades

Grade 12

Types

Teacher Tools, Lesson Plans

File

Microsoft PowerPoint

Editable
No
Author
Maths Support Centre
Rating
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About This Product

PowerPoint presentation, 19 slides explaining the use of basic rules to differentiate functions.

What's Included

PowerPoint presentation, 19 slides

Resource Tags

calculus derivative basic rules to differentiate differentiate functions

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