# Calculus/Differentiation/Basics of Differentiation/Exercises

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< Calculus | Differentiation

## Contents

## Find the Derivative by Definition[edit]

Find the derivative of the following functions using the limit definition of the derivative.

1.

2.

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9.

## Prove the Constant Rule[edit]

10. Use the definition of the derivative to prove that for any fixed real number ,

## Find the Derivative by Rules[edit]

Find the derivative of the following functions:

### Power Rule[edit]

11.

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### Product Rule[edit]

20.

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### Quotient Rule[edit]

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### Chain Rule[edit]

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### Exponentials[edit]

42.

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### Logarithms[edit]

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### Trigonometric functions[edit]

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## More Differentiation[edit]

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## Implicit Differentiation[edit]

Use implicit differentiation to find y'

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## Logarithmic Differentiation[edit]

Use logarithmic differentiation to find :

64.

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## Equation of Tangent Line[edit]

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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75. Find an equation of the tangent line to the graph defined by at the point (1,-1).

76. Find an equation of the tangent line to the graph defined by at the point (1,0).

## Higher Order Derivatives[edit]

77. What is the second derivative of ?

78. Use induction to prove that the

*(n+1)th*derivative of a*n-th*order polynomial is 0.