High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #57 : Calculus I — Derivatives

What is the second derivative of ?

Possible Answers:

Undefined

Correct answer:

Explanation:

To get the second derivative, first we need to find the first derivative.

To do that, we can use the power rule. That means we lower the exponent of the variable by one and multiply the variable by that original exponent.

We're going to treat  as , as anything to the zero power is one.

That means this problem will look like this:

Notice that  as anything times zero will be zero.

Remember, anything to the zero power is one.

Now to get the second derivative we repeat those steps, but instead of using , we use .

Notice that  as anything times zero will be zero.

Example Question #58 : Calculus I — Derivatives

What is the second derivative of ?

Possible Answers:

Correct answer:

Explanation:

To get the second derivative, first we need to find the first derivative.

To do that, we can use the power rule. That means we lower the exponent of the variable by one and multiply the variable by that original exponent.

We're going to treat  as , as anything to the zero power is one.

Notice that , as anything times zero is zero.

Now we repeat the process using  as the expression.

Just like before, we're going to treat  as .

Example Question #51 : Derivatives

If , what is ?

Possible Answers:

Correct answer:

Explanation:

The question is asking us for the second derivative of the equation. First, we need to find the first derivative.

To do that, we can use the power rule. To use the power rule, we lower the exponent on the variable and multiply by that exponent.

We're going to treat  as  since anything to the zero power is one.

Notice that  since anything times zero is zero.

Now we do the exact same process but using  as our expression.

As stated earlier, anything to the zero power is one.

Example Question #52 : Derivatives

What is the second derivative of ?

Possible Answers:

Undefined

Correct answer:

Explanation:

To find the second derivative, first we need to find the first derivative.

To do that, we can use the power rule. To use the power rule, we lower the exponent on the variable and multiply by that exponent.

We're going to treat  as  since anything to the zero power is one.

Notice that  since anything times zero is zero.

That leaves us with .

Simplify.

As stated earlier, anything to the zero power is one, leaving us with:

Now we can repeat the process using  or  as our equation.

As pointed out before, anything times zero is zero, meaning that .

 

Example Question #53 : Derivatives

What is the second derivative of ?

Possible Answers:

Correct answer:

Explanation:

To find the second derivative, first we need to find the first derivative.

To do that, we can use the power rule. To use the power rule, we lower the exponent on the variable and multiply by that exponent.

We're going to treat  as  since anything to the zero power is one.

Notice that  since anything times zero is zero.

Just like it was mentioned earlier, anything to the zero power is one.

Now we repeat the process using  as our expression.

Like before, anything times zero is zero.

Anything to the zero power is one.

Example Question #20 : Finding Second Derivative Of A Function

What is the second derivative of ?

Possible Answers:

Correct answer:

Explanation:

To find the second derivative, we need to find the first derivative.

To find the first derivative of the problem, we can use the power rule. The power rule says to multiply the coefficient of the variable by the exponent of the variable and then lower the value of the exponent by one.

To make that work, we're going to treat  as , since anything to the zero power is one.

This means that  is the same as .

Now use the power rule:

Anything times zero is zero.

Now we repeat the process, but using .

Since anything times zero is zero, 

Example Question #42 : General Derivatives And Rules

What is the second derivative of ?

Possible Answers:

Correct answer:

Explanation:

To start we need to find the first derivative. For that, we need to use the chain rule: 

Repeat the process!

Remember that :

Example Question #22 : Finding Second Derivative Of A Function

What is the second derivative of ?

Possible Answers:

Correct answer:

Explanation:

To find the second derivative, we need to start with the first derivative.

To find the first derivative of , we can use the power rule.

The power rule states that we multiply each variable by its current exponent and then lower the exponent of each variable by one.

Since , we're going to treat  as .

Anything times zero is zero, so our final term , regardless of the power of the exponent.

Simplify what we have.

Our first derivative, then, is .

To find the second derivative, we repeat the process using  for our equation.

Simplify.

Remember that , which means our second derivative will be .

Example Question #52 : Derivatives

If , what is ?

Possible Answers:

Correct answer:

Explanation:

To find , or the second derivative of our function, we need to start by finding the first derivative. 

To find the first derivative, we can use the power rule. The power rule states that we multiply each variable by its current exponent and then lower that exponent by one. 

Simplify.

Anything to the zero power is one, so .

Therefore, .

Now we repeat the process, but we use .

Remember, anything times zero is zero.

Example Question #54 : Derivatives

If  what is the slope of the line at .

Possible Answers:

Correct answer:

Explanation:

The slope at any point on a line is also equal to the derivative. So first we want to find the derivative function of this function and then evaluate it at. So, to find the derivative we will need to use the chain rule. The chain rule says

 so if we let  and  then

since  and 

 

Therefore we evaluate at  and we get  or .

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