Calculus 2 : Definition of Derivative

Study concepts, example questions & explanations for Calculus 2

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Example Questions

Example Question #51 : Definition Of Derivative

Find the derivative of  using the definition of the derivative.

Possible Answers:

Correct answer:

Explanation:

The definition of a derivative is 

Substituting these expressions into the definition of a derivative gives us

Substituting in the trigonometric identity 

Then using the identities

 and 

Example Question #52 : Derivative Review

Find the derivative of  using the definition of the derivative.

Possible Answers:

Correct answer:

Explanation:

The definition of a derivative is 

Substituting these expressions into the definition of a derivative gives us

Substituting in the trigonometric identity 

 

Then using the identities

 and 

Example Question #53 : Derivative Review

Find the derivative of  using the definition of the derivative.

Possible Answers:

Correct answer:

Explanation:

The definition of a derivative is 

Substituting these expressions into the definition of a derivative gives us

Example Question #54 : Derivative Review

Find the derivative of  using the definition of the derivative.

Possible Answers:

Correct answer:

Explanation:

The definition of a derivative is 

Substituting these expressions into the definition of a derivative gives us

 

 

Example Question #55 : Derivative Review

Find the derivative of  using the definition of the derivative.

Possible Answers:

Correct answer:

Explanation:

The definition of a derivative is 

Substituting these expressions into the definition of a derivative gives us

 

Example Question #51 : Derivative Review

Find the derivative of  using the definition of the derivative.

Possible Answers:

Correct answer:

Explanation:

The definition of a derivative is 

Substituting these expressions into the definition of a derivative gives us

Next we will multiply the numerator and denominator by the complex conjugate of the numerator

Example Question #51 : Definition Of Derivative

Find the derivative of  using the definition of the derivative.

Possible Answers:

Correct answer:

Explanation:

The definition of a derivative is 

Substituting these expressions into the definition of a derivative gives us

Example Question #58 : Derivative Review

Find the derivative of  using the definition of the derivative.

Possible Answers:

Correct answer:

Explanation:

The definition of a derivative is 

Substituting these expressions into the definition of a derivative gives us

Next we will multiply the numerator and denominator by the complex conjugate of the numerator

 

 

Example Question #59 : Derivative Review

Find the derivative of  using the definition of the derivative.

Possible Answers:

Correct answer:

Explanation:

The definition of a derivative is 

Substituting these expressions into the definition of a derivative gives us

Example Question #60 : Derivative Review

Find the derivative of  using the definition of the derivative.

Possible Answers:

Correct answer:

Explanation:

The definition of a derivative is 

Substituting these expressions into the definition of a derivative gives us

 

 

 

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