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Differentiationand Integrationof Logarithmicand ExponentialFunctions
LearningObjectives
A studentwill be able to:
- Understandand use the rulesof differentiationof logarithmicand exponentialfunctions.
- Understandand use the rulesof integrationof logarithmicand exponentialfunctions.
In this sectionwe will explorethe derivativesof logarithmicand exponentialfunctions.We will also see how
the derivativeof a one-to-onefunctionis relatedto its inverse.
The Derivativeof a LogarithmicFunction
Our goal at this pointto find an expressionfor the derivativeof the logarithmicfunction Recall
that the exponentialnumber is definedas
(wherewe havesubstituted for for convenience).Fromthe definitionof the derivativeof that
you alreadystudiedin Chapter2,