# High School Math : Finding Derivatives

## Example Questions

### Example Question #9 : Finding Second Derivative Of A Function

Let .

Find the second derivative of .

Explanation:

The second derivative is just the derivative of the first derivative. So first we find the first derivative of . Remember the derivative of is , and the derivative for  is .

Then to get the second derivative, we just derive this function again. So

### Example Question #10 : Finding Second Derivative Of A Function

Define .

What is ?

Explanation:

Take the derivative  of , then take the derivative of .

### Example Question #31 : General Derivatives And Rules

Define .

What is  ?

Explanation:

Take the derivative  of , then take the derivative of .

### Example Question #32 : General Derivatives And Rules

Define .

What is ?

Explanation:

Take the derivative  of , then take the derivative of .

### Example Question #33 : General Derivatives And Rules

Define .

What is ?

Explanation:

Rewrite:

Take the derivative  of , then take the derivative of .

### Example Question #34 : General Derivatives And Rules

What is the second derivative of ?

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.

Remember that anything to the zero power is one.

Now we do the same process again, but using  as our expression:

Notice that , as anything times zero will be zero.

Anything to the zero power is one.

### Example Question #35 : General Derivatives And Rules

What is the second derivative of ?

Undefined

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 #36 : General Derivatives And Rules

What is the second derivative of ?

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 ?

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 ?

Undefined

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 .