Calculus 1 : Other Differential Functions

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #21 : How To Find Differential Functions

Find   

Possible Answers:

Correct answer:

Explanation:






Example Question #21 : Other Differential Functions

Differentiate:

 with respect to .

Possible Answers:

Correct answer:

Explanation:

Apply the chain rule: differentiate the "outside" function first. Let .

Differentiate the "inside" function next.

Multiply these two functions to find the derivative of the original function.

Example Question #22 : How To Find Differential Functions

Evaluate 

Possible Answers:

Correct answer:

Explanation:

To integrate the function, integrate each term of the function. e.g., integrate  by increasing the exponent by 1 integer and dividing the term by this new integer: .

Do this for the rest to get .

But remember that every integration requires an arbitrary constant, . Thus, the integral of the function is 

Example Question #211 : Differential Functions

Integrate

Possible Answers:

Correct answer:

Explanation:

We can use trigonometric identities to transform integrals that we typically don't know how to integrate. 



Thus,

Example Question #24 : How To Find Differential Functions

Integrate

 

Possible Answers:

Correct answer:

Explanation:

We can use trigonometric identities to integrate functions we typically don't know how to integrate. 


Thus,

Example Question #25 : How To Find Differential Functions

Evaluate

 

Possible Answers:

Correct answer:

Explanation:

You can transform the limits of integration via u-substitution. 

Let


When
When 

Thus,





Example Question #27 : Other Differential Functions

Differentiate the function 

Possible Answers:

Correct answer:

Explanation:

Using the product rule for finding derivatives gives the answer.  

Example Question #212 : Differential Functions

Solve for  when 

Possible Answers:

Correct answer:

Explanation:

using the quotient rule: 

 

Foil

combine like-terms to simplify

Example Question #27 : How To Find Differential Functions

Solve for  when 

Possible Answers:

Correct answer:

Explanation:

Using the Product Rule:  and chain rule for trignometry functions: 

Simplify

Example Question #28 : How To Find Differential Functions

Find the derivative of 

Possible Answers:

Correct answer:

Explanation:

The quantity square root of  raised to the third is the same as .  Using the chain rule and power rule, the answer can be found.

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