Calculus/Differentiation/Basics of Differentiation/Exercises
< Calculus | Differentiation
Find the Derivative by DefinitionEdit
Find the derivative of the following functions using the limit definition of the derivative.
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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
Find the derivative of the following functions:
Power RuleEdit
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Product RuleEdit
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Quotient RuleEdit
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Chain RuleEdit
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ExponentialsEdit
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LogarithmsEdit
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Trigonometric functionsEdit
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More DifferentiationEdit
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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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Equation of Tangent LineEdit
For each function, , (a) determine for what values of the tangent line to is horizontal and (b) find an equation of the tangent line to at the given point.
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87. Find an equation of the tangent line to the graph defined by at the point (1,-1).
88. Find an equation of the tangent line to the graph defined by at the point (1,0).
Higher Order DerivativesEdit
89. What is the second derivative of ?
90. Use induction to prove that the (n+1)th derivative of a n-th order polynomial is 0.