### All High School Math Resources

## Example Questions

### Example Question #21 : Calculus I — Derivatives

What is the first derivative of ?

**Possible Answers:**

**Correct answer:**

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 #5 : General Derivatives And Rules

**Possible Answers:**

**Correct answer:**

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 : Finding Derivatives

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

**Possible Answers:**

**Correct answer:**

The average rate of change of on interval is

Substitute:

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

What is the derivative of ?

**Possible Answers:**

**Correct answer:**

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 #2 : Finding Derivatives

What is the derivative of ?

**Possible Answers:**

**Correct answer:**

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 #21 : Derivatives

What is the derivative of ?

**Possible Answers:**

**Correct answer:**

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 : General Derivatives And Rules

What is the derivative of ?

**Possible Answers:**

**Correct answer:**

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 : Derivative Defined As The Limit Of The Difference Quotient

**Possible Answers:**

**Correct answer:**

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 #2 : Concept Of The Derivative

What is the derivative of ?

**Possible Answers:**

**Correct answer:**

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 #2 : Concept Of The Derivative

What is the derivative of ?

**Possible Answers:**

**Correct answer:**

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.

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

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