Chapter 2: Differentiation
Section 2.2: Precise Definition of the Derivative
Example 2.2.2
Apply Definition 2.2.1 to , to obtain , .
Solution
Define the function
Control-drag Context Panel: Assign Function
Method 1
Write the mathematical notation for the derivative
Context Panel: Evaluate and Display Inline
Context Panel: Simplify≻Simplify
=
Method 2
Type and press the Enter key.
Context Panel: Differentiate≻With Respect To≻
Context Panel: Evaluate at a Point≻
Method 3
Expression palette: Differentiation template Apply to and press the Enter key.
Evaluate at as above.
Stepwise solutions
Tools≻Load Package: Student Calculus 1
Loading Student:-Calculus1
Apply the NewtonQuotient command.
Context Panel: Evaluate at a Point≻ (The difference quotient is returned simplified, so the limit is found by setting to zero.)
Application of Definition 2.2.1
Expression palette: Limit template Type the difference quotient
The difference quotients in Examples 2.2.1-3 each require different algebraic manipulations for the stepwise computation of the limit.
The difference quotient and its simplification
Write the difference quotient; Press the Enter key.
The stepwise simplification of the difference quotient, shown below, is a recital of "addition of fractions by finding a common denominator."
, where
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