Chapter 2: Differentiation
Section 2.7: Derivatives of the Trig Functions
Example 2.7.1
Evaluate ddt cosπ t.
Solution
In Maple, there are at least three ways to obtain the required derivative.
Initialize
Tools≻Load Package: Student Calculus 1
Loading Student:-Calculus1
Solution #1
Type the function to be differentiated.
Context Panel: Differentiate≻With Respect To≻t
cosπ t→differentiate−sinπtπ
Solution #2
Expression palette: Differentiation template
Context Panel: Evaluate and Display Inline
ⅆⅆ t cosπ t = −sinπtπ
Solution #3 (stepwise)
Expression palette: Differentiation template Select t as the differentiation variable and enter the function to be differentiated.
Context Panel: Student Calculus1≻All Solution Steps
ⅆⅆ tcosπ t→show solution stepsDifferentiation Stepsⅆⅆtcosπt▫1. Apply the chain rule to the term cosπt◦Recall the definition of the chain ruleⅆⅆtfgt=f'gtⅆⅆtgt◦Outside functionfv=cosv◦Inside functiongt=πt◦Derivative of outside functionⅆⅆvfv=−sinv◦Apply compositionf'gt=−sinπt◦Derivative of inside functionⅆⅆtgt=π◦Put it all togetherⅆⅆtfgtⅆⅆtgt=−sinπt⋅πThis gives:−sinπtπ
Alternatively, an interactive stepwise solution is available via the Context Panel, as shown in the figure to the right.
A stepwise solution can be generated interactively with the tutor. To apply a differentiation rule, click on the appropriate button. Figure 2.7.1(a) shows the tutor with a completed solution. Clicking the Close button returns an annotated version of this stepwise solution.
Figure 2.7.1(a) Differentiation Methods tutor applied to ddt cosπ t
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