Calculus 1 : Other Differential Functions

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #51 : How To Find Differential Functions

Differentiate the function using known derivatives and applying the product, quotient, and chain rules.

Possible Answers:

Correct answer:

Explanation:

We evaluate this derivative using the chain rule:

,

.

The outside function is:

 

The inside function is:

Therefore,

, which is our final answer.

 

 

Example Question #52 : Other Differential Functions

Solve the indefinite integral. If you cannot evaluate directly, use u-substitution.

Possible Answers:

Correct answer:

Explanation:

We use the trig identity .

, which is our final answer.

Example Question #51 : Other Differential Functions

Solve the indefinite integral. If you cannot evaluate directly, use u-substitution.

Possible Answers:

 + c

 + c

 + c

 + c

 + c

Correct answer:

 + c

Explanation:

.

, which is our final answer.

Example Question #52 : Other Differential Functions

Solve the indefinite integral. If you cannot evaluate directly, use u-substitution.

Possible Answers:

Correct answer:

Explanation:

.

, which is our final answer.

Example Question #53 : Other Differential Functions

Solve the indefinite integral. If you cannot evaluate directly, use u-substitution.

Possible Answers:

Correct answer:

Explanation:

We rewrite the denominator as a negative exponenet in the numerator to make the u-substitution easier to see:

, which is our final answer.

Example Question #56 : Other Differential Functions

Solve the indefinite integral. If you cannot evaluate directly, use u-substitution.

Possible Answers:

Correct answer:

Explanation:

 , which is our final answer.

Example Question #54 : Other Differential Functions

Solve the indefinite integral. If you cannot evaluate directly, use u-substitution.

Possible Answers:

Correct answer:

Explanation:

 , which is our final answer.

Example Question #51 : How To Find Differential Functions

Find the derivative of .

Possible Answers:

Correct answer:

Explanation:

The derivative of the difference of two functions is the difference of the derivative of the two functions:

     

Example Question #1271 : Calculus

Find the derivative of .

Possible Answers:

Correct answer:

Explanation:

We can write the function as

 .  

Let  .  

We then have 

.

Example Question #56 : Other Differential Functions

Differentiate the function:

Possible Answers:

Correct answer:

Explanation:

Using the chain rule, , ,

we observe the following:

.

.

, which is our final answer.

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