# High School Math : Finding Derivative of a Function

## Example Questions

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### Example Question #1 : Finding Derivative Of A Function

What is the first derivative of ?

Explanation:

To find the first derivative for this problem, we can use the power rule. The power rule states that we lower the exponent of each of the variables by one and multiply by that original exponent.

Remember that anything to the zero power is one.

### Example Question #1 : Finding Derivatives

Explanation:

This problem is best solved by using the power rule. For each variable, multiply by the exponent and reduce the exponent by one:

Treat as since anything to the zero power is one.

Remember, anything times zero is zero.

### Example Question #1 : General Derivatives And Rules

Give the average rate of change of the function  on the interval  .

Explanation:

The average rate of change of  on interval  is

Substitute:

### Example Question #1 : Derivative Defined As The Limit Of The Difference Quotient

What is the derivative of ?

Explanation:

To solve this problem, 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.

### Example Question #1 : Finding Derivative Of A Function

What is the derivative of ?

Explanation:

To solve this problem, 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 is zero.

Remember, anything to the zero power is one.

### Example Question #2 : Finding Derivative Of A Function

What is the derivative of ?

Explanation:

To solve this problem, 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.

### Example Question #1 : Finding Derivative Of A Function

What is the derivative of ?

Explanation:

To get , we can use the power rule.

Since the exponent of the  is , as , we lower the exponent by one and then multiply the coefficient by that original exponent:

Anything to the  power is .

### Example Question #1 : Finding Derivative Of A Function

Explanation:

To solve this equation, 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.

### Example Question #1 : Derivative Defined As The Limit Of The Difference Quotient

What is the derivative of ?

Explanation:

To solve this equation, 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:

### Example Question #3 : Finding Derivative Of A Function

What is the derivative of ?