Calculus 3 : Derivatives

Study concepts, example questions & explanations for Calculus 3

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Example Questions

Example Question #260 : Calculus 3

What is the derivative of ?

Possible Answers:

None of the Above

Correct answer:

Explanation:

Take the derivative of the first term:


Rewrite the other term with a(n) negative exponent:

Now, take the derivative of the re-written term:


Put both parts together:

Example Question #71 : Calculus Review

Find the derivative  given the function 

Possible Answers:

Correct answer:

Explanation:

We can find the derivative  given the function  by rewriting  as 

and using the properties of logarithms ( in particular) to get

so now we can use the chain rule

with  and  to get

Example Question #72 : Calculus Review

Find the derivative  of the function .

Possible Answers:

Correct answer:

Explanation:

We can find the derivative  of the function  by using the power rule for derivatives:

with  to get

Example Question #73 : Calculus Review

Find the derivative  of the function 

Possible Answers:

Correct answer:

Explanation:

We can find the derivative  of the function  by using the power rule for derivatives:

with  to get

Example Question #74 : Calculus Review

Find the derivative  of the function 

Possible Answers:

Correct answer:

Explanation:

We can find the derivative  of the function  by using the power rule for derivatives:

with  to get

Example Question #75 : Calculus Review

Find the derivative  of the function 

Possible Answers:

Correct answer:

Explanation:

We can find the derivative  of the function  by using the power rule for derivatives:

with  to get

Example Question #76 : Calculus Review

Find the derivative  of the function 

Possible Answers:

Correct answer:

Explanation:

We can find the derivative  of the function  by using the power rule for derivatives:

with  to get

Example Question #77 : Calculus Review

Find the derivative  of the function 

Possible Answers:

Correct answer:

Explanation:

We can find the derivative  of the function  by using the power rule for derivatives:

with  to get

Example Question #78 : Calculus Review

Find the derivative  of the function 

Possible Answers:

Correct answer:

Explanation:

We can find the derivative  of the function  by using the power rule for derivatives:

with  to get

Example Question #79 : Calculus Review

Find the derivative  of the function 

Possible Answers:

Correct answer:

Explanation:

We can find the derivative  of the function  by using the power rule for derivatives:

with  to get

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