Calculus 2 : Derivative Review

Study concepts, example questions & explanations for Calculus 2

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Example Questions

Example Question #101 : First And Second Derivatives Of Functions

Find the derivative of the function:

Possible Answers:

Correct answer:

Explanation:

The derivative of the function is equal to

and was found using the following rules:

Note that the radical acts as the "outer" function using the first rule, the chain rule.

Example Question #301 : Derivative Review

Find the derivative of the function:

Possible Answers:

Correct answer:

Explanation:

The derivative of the function is equal to

and was found using the following rules:

Example Question #103 : First And Second Derivatives Of Functions

Find the derivative of the function:

Possible Answers:

Correct answer:

Explanation:

The derivative of the function is equal to

and was found using the following rules:

Example Question #104 : First And Second Derivatives Of Functions

Find the derivative of the function:

Possible Answers:

Correct answer:

Explanation:

The derivative of the function is equal to

and was found using the following rules:

Example Question #105 : First And Second Derivatives Of Functions

Find the derivative of the function:

Possible Answers:

Correct answer:

Explanation:

The derivative of the function is equal to

and was found using the following rules:

Example Question #106 : First And Second Derivatives Of Functions

Find the first derivative of the function:

Possible Answers:

Correct answer:

Explanation:

The derivative of the function is equal to

and was found using the following rules:

,

Example Question #103 : First And Second Derivatives Of Functions

Find the second derivative of 

Possible Answers:

Correct answer:

Explanation:

To find the second derivative of a function, we must first find the first derivative. 

 Now, we must differentiate this function.  The first part is a straightforward trigonometric derivative.  For the second term, we must use the chain rule. 

Example Question #107 : First And Second Derivatives Of Functions

Find the derivative of .

Possible Answers:

Correct answer:

Explanation:

The derivative of  is special because it returns back the original function .  

Therefore, this derivative is simply a chain rule application of that exponential function. 

Recall the chain rule is,

Applying this rule to the original function results in the following derivative.

Example Question #108 : First And Second Derivatives Of Functions

Find the second derivative of 

Possible Answers:

Correct answer:

Explanation:

To get to the second derivative, we must first take the first derivative! 

 Then, we will differentiate that to get our answer.

Recall the trigonometric derivatives:

Example Question #302 : Derivative Review

What is the derivative of ?

Possible Answers:

Correct answer:

Explanation:

When taking the derivative, multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent. Therefore, the answer is:

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