Calculus/Differentiation/Basics of Differentiation/Solutions
< Calculus | Differentiation
Find the Derivative by DefinitionEdit
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Prove the Constant RuleEdit
10. Use the definition of the derivative to prove that for any fixed real number ,
Find the Derivative by RulesEdit
Power RuleEdit
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Product RuleEdit
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Quotient RuleEdit
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Chain RuleEdit
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Let . Then
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Let . Then
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Let . Then
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Let . Then
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Let . Then
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Let . Then
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Let . Then
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Let . Then
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Let . Then
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Let . Then
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Let . Then
ExponentialsEdit
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Let . Then
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Let
Then
Using the chain rule, we have
The individual factor are
So
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LogarithmsEdit
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Let . Then
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Trigonometric functionsEdit
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More DifferentiationEdit
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Let . Then
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Implicit DifferentiationEdit
Use implicit differentiation to find y'
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Logarithmic DifferentiationEdit
Use logarithmic differentiation to find :
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