Calculus 2 : First and Second Derivatives of Functions

Study concepts, example questions & explanations for Calculus 2

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Example Questions

Example Question #111 : First And Second Derivatives Of Functions

What is the derivative of ?

Possible Answers:

Correct answer:

Explanation:

Remember that when taking the derivative, multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent: . Simplify and make sure you don't have a negative exponent (to make it positive, put it in the denominator). Therefore, your answer is  .

Example Question #112 : First And Second Derivatives Of Functions

What is the derivative of

Possible Answers:

Correct answer:

Explanation:

Remember that when taking the derivative, multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent.

Therefore, your answer should look like this:

Example Question #113 : First And Second Derivatives Of Functions

What is the derivative of

Possible Answers:

Correct answer:

Explanation:

Recall that when taking the derivative, multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent.

Therefore, after differentiating, you get

.

Example Question #114 : 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 #115 : First And Second Derivatives Of Functions

Find the second derivative of the function

Possible Answers:

Correct answer:

Explanation:

To begin, you must take the first derivative of the function, which is:

Then, you take the derivative of the first derivative, which equals:

This simplifies to:

The rules of differentiation that were used are:

Example Question #116 : 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 the following:

and was found using the following rules:

Example Question #117 : First And Second Derivatives Of Functions

Find the first derivative of the function:

Possible Answers:

Correct answer:

Explanation:

The first derivative of the function is equal to:

and was found using the following rules:

Example Question #118 : First And Second Derivatives Of Functions

Find the second derivative of the function:

Possible Answers:

Correct answer:

Explanation:

The first derivative of the function is equal to

and was found using the following rules:

The second derivative of the function is equal to

and was found using the rules above, along with

Example Question #119 : First And Second Derivatives Of Functions

Find the derivative of the following function:

Possible Answers:

Correct answer:

Explanation:

The derivative of the function is equal to

and was found using the following rules:

 

Example Question #120 : First And Second Derivatives Of Functions

What is the derivative of ?

Possible Answers:

Correct answer:

Explanation:

To take the derivative, remember to multiply the exponent by the coefficient in front of the x term and then subtract one from the exponent:

Simplify and make the negative exponent positive by putting it on the denominator:

.

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